Answer:
c. results in either of two directions can lead to rejection of the null hypothesis.
Step-by-step explanation:
A two tailed test is performed when we want to test if there is statistically significant difference from the null state. That means that if the statistic value is significantly higher or significantly lower, we will reject the null hypothesis. Both tails have rejection areas.
Tara is graphing the equation 4x + 2y = 10. Which of these shows the correct equation in slope-intercept form, slope, and y-intercept?
Answer:
y = -2x + 5
slope = -2
y intercept = 5
Step-by-step explanation:
Slope intercept form of equation of line is given by y = mx + c
where m is the slope of line
c is the y intercept i.e point where given line intersect y axis.
________________________________________________
given equation 4x + 2y = 10
we have to re-write this equation in form y = mx + c
4x + 2y = 10
subtraction 4x from LHS and RHS
4x + 2y - 4x= 10 - 4x
2y = 10- 4x
we have to eliminate 2 from y for that we
divide LHS and RHS by 2 we
2y /2 = 10/2- 4x/2
y = 5 - 2x
rearranging it in y = mx+c form
y = -2x + 5
thus, m = -2 , c = 5
A water cooler holds 15 liters of sports drink. Approximately how many gallons is this
Which of the following describes the function x^3-8
Answer:
Is there any options if so just repost with the options and i will answer it
Step-by-step explanation:
What is X:
3x−22=44
5/6 = 10/2x−3
Answer:
x = 22
x = 4,6
Step-by-step explanation:
3x - 22 = 44
3x = 44 + 22
3x = 66
x = 66/3
x = 22
5/6 = 10/2x - 3
5/6 + 3 = 10/2x
5/6 + 18/6 = 10/2x
23/6 = 10/2x
23/6 * 2 = 10x
46 = 10x
x = 46/10
x = 4,6
find the LCM
of
75, 5,3
Answer:
LCM = 75
Step-by-step explanation:
1: Multiply the factor by the greatest number
Description:
The least common multiple for 75,5,3 is 75.
LCM= Least common Multiple
Please mark brainliest
Hope this helps.
Answer:
75
Step-by-step explanation:
Break each number into prime factors
75 = 25*3 = 5*5*3
5 = 5*1
3 = 3*1
Multiply by the greatest number of each factor
3 = 1 time
5 = =2 times
The least common multiple = 3 * 5*5 = 75
Write a linear function f with f(−2)=6 and f(0)=−4 .
Answer:
y = -5(x) - 4
Step-by-step explanation:
Use the equation of a line and substitution.
Information given:
point 1: (-2,6)
x1 = -2 and y1 = 6
point 2: (0,4)
x2 = 0 and y2 = 4
Equation of a line: y = m(x) + b
m = slope
To find slope, you do the equation of a linear slope, which is:
m = [tex]\frac{rise}{run}[/tex] in other words m = [tex]\frac{Y2 - Y1}{X2-X1}[/tex]
plug in your values
[tex]\frac{6-(-4)}{-2-0}[/tex]
= -5
Great, we've found slope, now to find b
plug in the slope you found: y = -5(x) + b
Plug in and solve for each point given, aka (x,y) into the linear equation for both points.
FIRST POINT:
6 = -5(-2) + b
6 = 10 + b
6 - 10 = b
b = -4
SECOND POINT:
-4 = -5(0) + b
-4 = 0 + b
-4 - 0 = b
b = -4
We got -4 for both, meaning that this equation is correct, so if you add in b, your final equation will be y = -5(x) - 4.
Plug this into desmos.com/calculator, and you'll see this linear equation runs through both points given in the problem.
Answer:
f(x)=-5x-4
Step-by-step explanation:
You are given two points (-2, 6) and (0, -4)
Find the slope: m=(-4-6)/[(0-(-2)]=-5
So you have y=-5x+b
next, find the y intercept b.
the y intercept is when x=0. in this case, the y intercept is -4
so the linear function is f(x)=-5x-4
What’s the correct answer for this question?
Answer:
A
Step-by-step explanation:
Volume of cone = (1/3) πr²h
Is a measure of 22 inches "far away" from a mean of 16 inches? As someone with knowledge of statistics, you answer "it depends" and request the standard deviation of the underlying data. (a) Suppose the data come from a sample whose standard deviation is 2 inches. How many standard deviations is 22 inches from 16 inches? (b) Is 22 inches far away from a mean of 16 inches? (c) Suppose the standard deviation of the underlying data is 4 inches. Is 22 inches far away from a mean of 16 inches?
Answer:
a) 3 standard deviations above 16
b) More than 2 standard deviations of the mean, so yes, 22 inches is faw away from the mean of 16 inches.
c) Less than 2 standard deviations, so not far away.
Step-by-step explanation:
Z-score:
In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the zscore of a measure X is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.
If Z < -2 or Z > 2, X is considered to be far away from the mean.
In this question, we have that:
[tex]\mu = 16[/tex]
(a) Suppose the data come from a sample whose standard deviation is 2 inches. How many standard deviations is 22 inches from 16 inches?
This is Z when [tex]X = 22, \sigma = 2[/tex].
So
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{22 - 16}{2}[/tex]
[tex]Z = 3[/tex]
So 22 inches is 3 standard deviations fro 16 inches.
(b) Is 22 inches far away from a mean of 16 inches?
3 standard deviations, more than two, so yes, 22 inches is far away from a mean of 16 inches.
(c) Suppose the standard deviation of the underlying data is 4 inches. Is 22 inches far away from a mean of 16 inches?
Now [tex]\sigma = 4[/tex]
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{22 - 16}{4}[/tex]
[tex]Z = 1.5[/tex]
1.5 standard deviations from the mean, so 22 inches is not far away from the mean.
Which of the following statements best describes the concept of a function?
Group of answer choices
For a given input value, there is, at most, one output value.
For a given output value, there is, at most, one input value.
For a given input value, there may be more than one output value.
There is no relationship between the input and output values.
Answer:
For a given output value, there is, at most, one input value
Step-by-step explanation:
Given: the concept of function
To find: the statement that best describes the concept of a function
Solution:
A function is a relation in which every value of the domain has a unique image in the codomain.
Input value belongs to the domain and output value belongs to the codomain.
The statement ''For a given output value, there is, at most, one input value'' describes the concept of a function
The statement best describes the concept of a function is
For a given output value, there is, at most, one input value.
Function :
A relation is a function when each input has exactly only one output
Concept :Domain x is the input and range y is the output
In a function , each input x must have exactly only one output.
Input x cannot have two outputs.
The statement best describes the concept of a function is
For a given output value, there is, at most, one input value.
Learn more information about 'functions' here :
brainly.com/question/1593453
An OSU senior is studying for exams in psychology and economics. The student has time to read 50 pages of psychology and 10 pages of economics. Or, in the same amount of time the student could read 30 pages of psychology and 70 pages of economics. How many pages of economics can the student read instead of reading just 1 page of psychology
Answer:
3 Pages
Step-by-step explanation:
Let the pages of economics read = eLet the pages of psychology read = pLet the total time taken on each instance=tIn the first instance, the student has time to read 50 pages of psychology and 10 pages of economics.
t=50p+10eThe student could read 30 pages of psychology and 70 pages of economics.
t=30p+70eSince the two situations take the same amount of time, we have:
50p+10e=30p+70e
Collect like terms
50p-30p=70e-10e
20p=60e
Divide both sides by 20
p=3e
Therefore, in the time it will take the student to read 1 page of psychology, the student can read 3 pages of economics.
Solve for x
A) 5
B) 6
C)7
D)8
Answer:
[tex]7x+1+6x+101=180\\13x=78\\x=6[/tex]
help me about this integral
The gradient theorem applies here, because we can find a scalar function f for which ∇ f (or the gradient of f ) is equal to the underlying vector field:
[tex]\nabla f(x,y,z)=\langle2xy,x^2-z^2,-2yz\rangle[/tex]
We have
[tex]\dfrac{\partial f}{\partial x}=2xy\implies f(x,y,z)=x^2y+g(y,z)[/tex]
[tex]\dfrac{\partial f}{\partial y}=x^2-z^2=x^2+\dfrac{\partial g}{\partial y}\implies\dfrac{\partial g}{\partial y}=-z^2\implies g(y,z)=-yz^2+h(z)[/tex]
[tex]\dfrac{\partial f}{\partial z}=-2yz=-2yz+\dfrac{\mathrm dh}{\mathrm dz}\implies\dfrac{\mathrm dh}{\mathrm dz}=0\implies h(z)=C[/tex]
where C is an arbitrary constant.
So we found
[tex]f(x,y,z)=x^2y-yz^2+C[/tex]
and by the gradient theorem,
[tex]\displaystyle\int_{(0,0,0)}^{(1,2,3)}\nabla f\cdot\langle\mathrm dx,\mathrm dy,\mathrm dz\rangle=f(1,2,3)-f(0,0,0)=\boxed{-16}[/tex]
The Toylot company makes an electric train with a motor that it claims will draw an average of only 0.8 ampere (A) under a normal load. A sample of nine motors was tested, and it was found that the mean current was x= 1.22 A, with a sample standard deviation of s = 0.44 A. Do the data indicate that the Toylot claim of 0.8 A is too low? (Use a 1% level of significance.)
1. What are we testing in this problem?
a. single proportion
b. single mean
2. What is the level of significance?
3. State the null and alternate hypotheses.
4. What sampling distribution will you use? What assumptions are you making?
a. The Student's t, since we assume that x has a normal distribution with known σ
b. The standard normal, since we assume that x has a normal distribution with known σ.
c. The standard normal, since we assume that x has a normal distribution with unknown σ.
d. The Student's t, since we assume that x has a normal distribution with unknown σ.
Answer:
1. B
Step-by-step explanation:
1. We are testing against the null hypothesis which is a single mean that sauce the average load is 0.8A
2. The level of significance is 1% (99% confidence interval)
3. The null hypothesis: u = 0.8
Alternative hypothesis: u =/ 0.8
4. a. The Student's t, since we assume that x has a normal distribution with known σ
5. Using the formula t = (x - u) / σ√n
Where x = 1.22 u = 0.8 σ = 0.44 n = 9
t = (1.22-0.8) / 0.44√9
t = 0.42/(0.44x3)
t = 0.42/1.32
t = 0.318
P value for 0.318 at 1% level of significance at 8 degree of freedom is 0.7586. Since our p value here is greater than 0.01, we can convince that there is not enough statistical evidence that indicate that the Toylot claim of 0.8 A is too low.
g You flip the coin 200 times and observed 80 Heads. Recall from the problem Hypothesis Testing: A Sample Data Set of Coin Flips I in the previous lecture that the value of the test statistics Tn for this data set is T200=2.83 . If the test ψ=1(Tn>qα/2) is designed to have asymptotic level 5% , would you reject or fail to reject the null hypothesis H0:p∗=1/2 for this data set?
Answer:
Step-by-step explanation:
To be able to draw a conclusion from the data given, lets find out the p value using the t score and this will be used to make a conclusion.
If the p value is less than 0.05 then, we will reject the null but if otherwise we will fail to reject the null.
Using a p value calculator with a t score of 2.83, significance level 0.05 and the test is a two tailed test, the p value is 0.004655 which is less than 0.05 and the result is significant.
This we will reject the null hypothesis H0:p∗=1/2 for this data set.
(X+3)/6=5/4 what is x
Answer:
x = 9/2
Step-by-step explanation:
(x+3)/6=5/4
(x+3)/6*6=5/4*6
x+3=30/4
x+3-3=30/4-3
x=9/2
250cm3 of fresh water of density 1000kgm-3 is mixed with 100cm3 of sea water of density 1030kgm-3. Calculate the density of the mixture. *
Answer:
[tex] m_{fresh}= 1000 \frac{Kg}{m^3} * 2.5x10^{-4} m^3 = 0.25 Kg[/tex]
And we can do a similar procedure for the sea water:
[tex] m_{sea}= \rho_{sea} V_{sea} [/tex]
And after convert the volume to m^3 we got:
[tex] m_{sea}= 1030 \frac{Kg}{m^3} * 1x10^{-4} m^3 = 0.103 Kg[/tex]
And then the density for the mixture would be given by:
[tex] \rho_{mixture}= \frac{m_{fresh} +m_{sea}}{v_{fresh} +v_{sea}}[/tex]
And replacing we got:
[tex] \rho_{mixt}= \frac{0.25 +0.103 Kg}{2.5x10^{-4} m^3 +1x10^{-4} m^3} = 1008.571 \frac{Kg}{m^3}[/tex]
Step-by-step explanation:
For this case we can begin calculating the mass for each type of water:
[tex] m_{fresh}= \rho_{fresh} V_{fresh} [/tex]
And after convert the volume to m^3 we got:
[tex] m_{fresh}= 1000 \frac{Kg}{m^3} * 2.5x10^{-4} m^3 = 0.25 Kg[/tex]
And we can do a similar procedure for the sea water:
[tex] m_{sea}= \rho_{sea} V_{sea} [/tex]
And after convert the volume to m^3 we got:
[tex] m_{sea}= 1030 \frac{Kg}{m^3} * 1x10^{-4} m^3 = 0.103 Kg[/tex]
And then the density for the mixture would be given by:
[tex] \rho_{mixture}= \frac{m_{fresh} +m_{sea}}{v_{fresh} +v_{sea}}[/tex]
And replacing we got:
[tex] \rho_{mixt}= \frac{0.25 +0.103 Kg}{2.5x10^{-4} m^3 +1x10^{-4} m^3} = 1008.571 \frac{Kg}{m^3}[/tex]
Jose predicted that he would sell 48 umbrellas. He actually sold 72 umbrellas.What are the values of a and b in the table below. Round to the nearest tenth if necessary
Answer:
The answer is A
Step-by-step explanation:
Solve (x + 1 < 4) ∩ (x - 8 > -7).
Answer:
[tex]1<x<3[/tex]
Step-by-step explanation:
Let simplify each of these inequalities individually and then look at where they intersect afterwards
[tex]x+1<4\\\\x<3[/tex]
And
[tex]x-8>-7\\\\x>1[/tex]
This means that for these two inequalities to intersect, x must be greater than 1, but less than 3.
This can be represented by the following inequality [tex]1<x<3[/tex]
When each of the following is divided by 8, only ?_ has a remainder that is a prime number. A) 548 B) 569 C) 678 D) 778
Answer:
the answer you are looking for is D 778
Fuel Efficiency of Cars and Trucks Since 1975 the average fuel efficiency of U.S. cars and light trucks (SUVs) has increased from 13.5 to 25.8 mpg, an increase of over 90%! A random sample of 40 cars from a large community got a mean mileage of 28.1 mpg per vehicle. The population standard deviation is 4.7 mpg. Estimate the true mean gas mileage with 95% confidence.
Answer:
[tex]28.1-1.96\frac{4.7}{\sqrt{40}}=26.64[/tex]
[tex]28.1+ 1.96\frac{4.7}{\sqrt{40}}=29.56[/tex]
We are confident at 95% of confidence that the true mean for the mpg is between 26.64 and 29.56. And since the lower limit from the confidence interval is highert than 25.8 then we can conclude that we have a significant increase from 1975
Step-by-step explanation:
Information given
[tex]\bar X= 28.1[/tex] represent the sample mean
[tex]\mu[/tex] population mean
[tex]\sigma =4.7[/tex] represent the population standard deviation
n=40 represent the sample size
Confidence interval
The confidence interval for the mean is given by the following formula:
[tex]\bar X \pm z_{\alpha/2}\frac{\sigma}{\sqrt{n}}[/tex] (1)
The Confidence level is is 0.95 or 95%, the significance would be [tex]\alpha=0.05[/tex] and [tex]\alpha/2 =0.025[/tex], and we can calculate the critical value using the normal standard distribution and we got [tex]z_{\alpha/2}=1.96[/tex]
And replacing we got:
[tex]28.1-1.96\frac{4.7}{\sqrt{40}}=26.64[/tex]
[tex]28.1+ 1.96\frac{4.7}{\sqrt{40}}=29.56[/tex]
We are confident at 95% of confidence that the true mean for the mpg is between 26.64 and 29.56. And since the lower limit from the confidence interval is highert than 25.8 then we can conclude that we have a significant increase from 1975
Consider the following data representing the price of laptop computers (in dollars). 12041204, 12061206, 13451345, 13061306, 12071207, 10781078, 13571357, 12321232, 12281228, 13021302, 11891189, 11771177, 10831083, 10941094, 13261326, 10711071, 14271427, 13481348, 14201420, 12531253, 1270 Determine the frequency of the fifth class.
Answer:
Step-by-step explanation:
The given data is expressed as
1204, 1206, 1345, 1306, 1207, 1078, 1357, 1232, 1228, 1302, 1189, 1177, 1083, 1094, 1326, 1071, 1427, 1348, 1420, 1253, 1270
The number of items in the data, n is 21. The lowest value is 1071 while the highest value is 1427. The convenient starting point would be 1070.5 and the convenient ending point would be 1427.5
The number of class intervals is
√n = √21 = 4.5
Approximately 5
The width of each class interval is
(1427.5 - 1070.5)/5 = 72
The end of each class interval would be
1070.5 + 72 = 1142.5
1142.5 + 72 = 1214.5
1214.5 + 72 = 1286.5
1286.5 + 72 = 1358.5
1358.5 + 72 = 1430.5
The frequency for the fifth class, that is between 1358.5 to 1430.5 would be 2
I WILL GIVE BRAINLIEST PLEASE ANSWER ASAP!!!
If the measure of angle 2 is (5 x + 14) degrees and angle 3 is (7 x minus 14) degrees, what is the measure of angle 1 in degrees?
2 lines intersect to form 4 angles. From top left, clockwise, the angles are 1, 2, 3, 4.
88 degrees
89 degrees
90 degrees
91 degrees
Answer:
<1 = 91
Step-by-step explanation:
<2 + <3 = 180
5 x + 14 + (7 x -14) = 180
Combine like terms
12x = 180
Divide by 12
12x/12 = 180/12
x =15
We want <1
<1 = <3 since they are vertical angle
<1 = 7x-14 = 7*15 -14 =105-14=91
Answer:
D, 91 degrees
Step-by-step explanation:
First, solve for x. Angles 2 and 3 add up to 180, so set up an equation:
(5x + 14) + (7x - 14) = 180
12x = 180
x = 15
Then, you know angles 1 and 2 also add up to 180, so solve for Angle 2
5(15) + 14= 89
180-89= 91, so angle 1 is 91 degrees.
The pressure p(in lbs/in^2) that a 160 pound persons shoe exerts on the ground when walking varies inversely with the area A(in in^2) of the sole of the shoe when the shoes have a sole area of 40 in^2 The pressure is 4 lbs/in^2 find equation that relates these variables
A=
Answer:
[tex]A = \dfrac{40}{P}[/tex]
Step-by-step explanation:
Pressure [tex]p(in lbs/in^2)[/tex] varies inversely with the area [tex]A(in$ in^2)[/tex] of the sole of the shoe.
This is written as:
[tex]P \propto \frac{1}{A}\\ $Introducing the constant of variation$\\P = \dfrac{k}{A}[/tex]
When:
[tex]When: A= 40 in^2, P =4 lbs/in^2\\$Substituting into the equation\\P = \dfrac{k}{A}\\4 = \dfrac{k}{40}\\$Cross multiply\\k=4*40\\k=160\\Therefore, the equation that connect these variables is given as:\\P = \dfrac{40}{A}\\$In terms of P\\AP=40\\\\A = \dfrac{40}{P}[/tex]
Which explains how to find the quotient of the division below? - 3 1/3 divided by 4/9 Write Negative 3 and one-third as Negative StartFraction 13 over 3 EndFraction, and find the reciprocal of StartFraction 4 over 9 EndFraction as StartFraction 9 over 4 EndFraction. Then, rewrite Negative 3 and one-third divided by StartFraction 4 over 9 EndFraction as Negative StartFraction 13 over 3 EndFraction times StartFraction 9 over 4 EndFraction. The quotient is Negative 9 and three-fourths. Write Negative 3 and one-third as Negative StartFraction 10 over 3 EndFraction, and find the reciprocal of StartFraction 4 over 9 EndFraction as StartFraction 9 over 4 EndFraction. Then, rewrite Negative 3 and one-third divided by StartFraction 4 over 9 EndFraction as Negative StartFraction 10 over 3 EndFraction times StartFraction 9 over 4 EndFraction. The quotient is Negative 7 and StartFraction 6 over 12 EndFraction = Negative 7 and one-half. Write Negative 3 and one-third as Negative StartFraction 9 over 3 EndFraction. Then, rewrite Negative 3 and one-third divided by StartFraction 4 over 9 EndFraction as Negative StartFraction 9 over 3 EndFraction times StartFraction 4 over 9 EndFraction. The quotient is Negative 1 and one-third. Write Negative 3 and one-third as Negative StartFraction 10 over 3 EndFraction. Then, rewrite Negative 3 and one-third divided by StartFraction 4 over 9 EndFraction as Negative StartFraction 10 over 3 EndFraction times StartFraction 4 over 9 EndFraction. The quotient is Negative 1 and StartFraction 13 over 27 EndFraction = Negative 1 and StartFraction 13 over 27 EndFraction
Answer:
The answer is D
Step-by-step explanation:
Answer:
A
Step-by-step explanation:
A parabola has a focus of (6,–6) and a directrix of y = –2. Which of the following could be the equation of the parabola?
Answer:
[tex]-8(y+4) =(x-6)^{2}[/tex]
Step-by-step explanation:
The standard form of a parabola is given by the following equation:
[tex](x-h)^{2} =4p(y-k)[/tex]
Where the focus is given by:
[tex]F(h,k+p)[/tex]
The vertex is:
[tex]V=(h,k)[/tex]
And the directrix is:
[tex]y-k+p=0[/tex]
Now, using the previous equations and the information provided by the problem, let's find the equation of the parabola.
If the focus is (-6,6):
[tex]F=(h,k+p)=(6,-6)[/tex]
Hence:
[tex]h=6\\\\k+p=-6\hspace{10}(1)[/tex]
And if the directrix is [tex]y=-2[/tex] :
[tex]-2-k+p=0\\\\k-p=-2\hspace{10}(2)[/tex]
Using (1) and (2) we can build a 2x2 system of equations:
[tex]k+p=-6\hspace{10}(1)\\k-p=-2\hspace{10}(2)[/tex]
Using elimination method:
(1)+(2)
[tex]k+p+k-p=-6+(-2)\\\\2k=-8\\\\k=-\frac{8}{2}=-4\hspace{10}(3)[/tex]
Replacing (3) into (1):
[tex]-4+p=-6\\\\p=-6+4\\\\p=-2[/tex]
Therefore:
[tex](x-6)^{2} =4(-2)(y-(-4)) \\\\(x-6)^{2} =-8(y+4)[/tex]
So, the correct answer is:
Option 3
Please answer this correctly
Answer:
452
Step-by-step explanation:
plz mark brainliest!
Answer:
i'll say you have to multiple 9 by 9 than 5 by 5 BUT 23 25 13 and 7 IDK sorry hope i helped :)
Step-by-step explanation:
Express the function G in the form f∘g. (Enter your answers as a comma-separated list. Use non-identity functions for
f(x) and g(x).)
Answer:
i dont really know what it is
A small-business Web site contains 100 pages and 60%, 30%, and 10% of the pages contain low, moderate, and high graphic content, respectively. A sample of four pages is selected without replacement, and X and Y denote the number of pages with moderate and high graphics output in the sample. Determine: a. fxy(x, y) b. fx(x) c. E(X) d. fyß(y) e. E(Y | X = 3) g. Are X and Y independent?
Answer:
Step-by-step explanation:
Given that:
A small-business Web site contains 100 pages and 60%, 30%, and 10% of the pages contain low, moderate, and high graphic content, respectively.
. A sample of four pages is selected without replacement,
Let X and Y denote the number of pages with moderate and high graphics output in the sample
We are meant to determine
a) [tex]f_{XY}(x, y)[/tex] from the given data in the question;
However; the probability mass function can be expressed via the relation:
[tex]f_{XY}(x,y) = \dfrac{(^{30} _x ) ( ^{10} _y ) (^{60} _ {4-x-y} ) }{ ( ^{100}_4)}[/tex]
We can now have a table shown as :
[tex]X|Y[/tex] 0 1 2 3 4 Total [tex]f_X(x)[/tex]
0 0.1244 0.0873 0.02031 0.0018 0.0001 0.234
1 0.2618 0.13542 0.02066 0.00092 0 0.419
2 0.1964 0.0666 0.00499 0 0 0.268
3 0.0621 0.01035 0 0 0 0.073
4 0.0069 0 0 0 0 0.007
Total [tex]F_Y(y)[/tex] 0.6516 0.2996 0.0460 0.0028 0.0001 1
b) [tex]f_X(x)[/tex]
The marginal distribution definition of [tex]f_X(x)[/tex][tex]= P(X=x)[/tex]
[tex]f_X(x)[/tex] [tex]= \sum P(X=x, Y=y)[/tex]
From the table above ; the corresponding values of [tex]f_X(x)[/tex] are :
X 0 1 2 3 4
[tex]f_X(x)[/tex] 0.234 0.419 0.268 0.073 0.007
( since [tex]f_X(x)[/tex] represent the vertical column)
c) E(X)
By using the expression [tex]E(x) = \sum ^4 _{x= 0} x f_X(x)[/tex]
we have:
E(X) = [tex]0*0.234+1*0.419+ 2*0.268+3*0.073+4*0.007[/tex]
E(X) = 0 + 0.419 + 0.536 + 0.218 + 0.028
E(X) = 1.202
d) fyß(y)
Using the thesis of conditional Probability; we have :
[tex]P(A|B) = \dfrac{ P(A,B) }{ P(B) }[/tex]
The conditional probability for the mass function is then:
[tex]f_{Y|X=3}(y) = \dfrac{f_{XY}(3,y)}{f_{X}(x)}[/tex]
where;
[tex]f_X(3) = 0.0725[/tex]
values of [tex]f_{XY} (3,y)[/tex] for every y ∈ (0,1,2,3,4)
Therefore; the mass function is:
[tex]Y|{_X_3}:\left[\begin{array}{ccccc}0&1&2&3&4\\0.857&0.143&0&0&0\\ \end{array}\right][/tex]
e) E(Y | X = 3)
By using the expression [tex]E(Y|X=3) = \sum ^4 _{y= 0} y f_{y \beta} \ (y|x)[/tex]
we have:
⇒ [tex]0 * 0.857 + 1*0.143 +0 +0+0[/tex]
= 0.143
The value of E(Y | X = 3) = 0.143
g) Are X and Y independent?
To Check if X and Y independent; Let assume if [tex]f_{XY}(x,y) = f_X(x)f_{Y}(y)[/tex] ; then we can say that X and Y are independent.
From the above previous table :
[tex]f_{(XY)} (0.4) = 0.0001[/tex]
[tex]f_X (0)[/tex] = 0.1244 + 0.087268+0.02031+ 0.001836 + 0.0001
[tex]f_X (0)[/tex] = 0.234
[tex]f_X (4)=0.0001 +0+0 \\ \\ = 0.001[/tex]
[tex]f_{X}(0) f_Y(4) = 0.234*0.0001[/tex]
[tex]f_{X}(0) f_Y(4) = 0.00002[/tex]
We conclude that [tex]f_{(XY)} (0.4) \neq f_X(0) f_Y(y)[/tex]; As such X and Y are said to be non - independent.
Question: A box contains 160 Iphone XR's.
60% of the IPhones are Forest Green.
How many IPhones are Forest Green?
Answer:
96
Step-by-step explanation:
60% * 160 = 0.6 * 160 = 96.
Answer:
None
Step-by-step explanation:
There is no Forest Green iPhone XR's only the 11 Pros have that color.
Alex and Bryan are giving an exam. The probability Alex gets an A is 0.9, the probability Bryan gets an A is 0.8 and the probability Alex gets an A and Bryan doesn't get an A is 0.1. What is the probability that either Alex or Bryan get an A.
Answer:
The probability that either Alex or Bryan get an A is 0.9
Step-by-step explanation:
Before we proceed to answer, we shall be making some important notation;
Let A = event of Alex getting an A
Let B = event of Bryan getting an A
From the question, P(A) = 0.9, P(B) = 0.8 and P(A ∩ [tex]B^{c}[/tex] ) = 0.1
We are to calculate the probability that either Alex or Bryan get an A which can be represented as P(A ∪ B)
We can use the addition theorem here;
P(A ∪ B) = P(A) + P(B) - P(A ∩ B) .......................(i)
Also,
P(A) = P(A ∩ [tex]B^{c}[/tex] ) + P(A ∩ B) .........................(ii)
We can insert ii into i and we have;
P(A ∪ B) = P(A ∩ [tex]B^{c}[/tex] ) + P(A ∩ B) + P(B) - P(A ∩ B) = P(A ∩ [tex]B^{c}[/tex] ) + P(B) = 0.1 + 0.8 = 0.9
