Problem 3.3.9 • (a) Starting on day 1, you buy one lottery ticket each day. Each ticket is a winner with probability 0.1. Find the PMF of K, the number of tickets you buy up to and including your fifth winning ticket. (b) L is the number of flips of a fair coin up to and including the 33rd occurrence of tails. What is the PMF of L? (c) Starting on day 1, you buy one lottery ticket each day. Each ticket is a winner with probability 0.01. Let M equal the number of tickets you buy up to and including your first winning ticket. What is the PMF of M?

Answers

Answer 1

Answer:

a) The probability mass function of K = [tex]P(K=k) = \binom{k-1}{4}0.1^{4}*0.9^{k-5} ; k =5,6,...[/tex]

b)

c)

Step-by-step explanation:

a) Let p be  the probability of winning each ticket be = 0.1

Then q which is the probability of failing each ticket  = 1 - p = 1  - 0.1 = 0.9

Assume X represents the  number of failure preceding the 5th success in x + 5 trials.

The last trial must be success whose probability is p = 0.1 and in the remaining (x + r- 1) ( x+ 4 ) trials we must have have (4) successes whose probability is given by:

[tex]\binom{x+r-1}{r-1}*p^{r-1}*q^{x} = \binom{x+4}{4}0.1^{4}*0.9^{x} ; x =0, 1, .........[/tex]

Then, the probability distribution of random variable X is

[tex]P(X=x) = \binom{x+4}{4}0.1^{4}*0.9^{x} ; x =0, 1, .........[/tex]

where;

X represents the  negative binomial random variable.

K= X + 5 = number of ticket buy up to and including fifth winning ticket.

Since K =X+5 this signifies that  X = K-5

as X takes value 0, 1 ,2,...

K takes value 5, 6 ,...

Therefore:

The probability mass function of K = [tex]P(K=k) = \binom{k-1}{4}0.1^{4}*0.9^{k-5} ; k =5,6,...[/tex]

b)

Let p represent the probability of getting a tail on a flip of the coin

Thus p = 0.5 since it is a fair coin

where L = number of flips of the coin including 33rd occurrence of  tails

Thus; the negative binomial distribution of L can be illustrated as:

[tex]P(X=x) = \binom{x-1}{r-1}(1-p)^{x-r}p^r[/tex]

where

X= L

r = 33  &

p = 0.5

Since we are looking at the 33rd success; L is likely to be : L = 33,34,35...

Thus; the PMF of L = [tex]P(L=l) = \binom{l-1}{33-1}(1-0.5)^{l}(0.5)^{33} \\ \\ \\ \mathbf{P(L=l) = \binom{l-1}{33-1}(0.5)^{l} }[/tex]

c)  

Given that:

Let  M be the random variable which represents  the number of tickets need to be bought to get the first success,

also success probability is 0.01.

Therefore, M ~ Geo(0.01).

Thus, the PMF of M is given by:

[tex]P(M = m) = (1-0.01)^{m-1} * 0.01 , \ \ \ since \ \ \ (m = 1,2,3,4,....)[/tex]

[tex]P(M=m) = (0.99)^{m-1} * 0.01 , m = 1,2,3,4,....[/tex]


Related Questions

Find the produce 2 1/3 times 3 1/2

Answers

Answer:

49/6 or 8 16/99

Step-by-step explanation:

2 1/3 *3 1/2 = (7/3*7/2)= 49/6

First convert to fraction form

then multiply across numerator to numerator and denominator to deominator

Simplify if needed

Turn to mixed fraction if needed

What is the area of the obtuse triangle below?
A. 90 sq units
B. 23 sq units
C. 18 sq units
D. 45 sq units

Answers

Answer:

A. 90 sq. units

Step-by-step explanation:

5(18) = 90

The area of a circle is 153.86 square meters. What is the diameter of the circle? Use 3.14 for π.

Answers

Answer:

14m

Step-by-step explanation:

The area of a circle is given by

A = pi r^2

153.86 = 3.14 r^2

Divide each side by  3.14

153.86 /3.14 = r^2

49 = r^2

Take the square root of each side

sqrt(49) = sqrt(r^2)

7 = r

We want the diameter which is twice the radius

d = 2r

d =2*7

d =14

Answer:

I just wanted to add on it is 14 i tried it on savaas and it worked

Step-by-step explanation:

Solve for y=x squared -18 solve for x

Answers

Step-by-step explanation:

[tex]y = {x}^{2} - 18 \\ y + 18 = {x}^{2} \\ square \: root \: both \: sides \: \\ \sqrt{y + 18} = \sqrt{ {x}^{2} } [/tex]

[tex]x = \sqrt{y + 18} [/tex]

Answer:

√y + 18 = x

Step-by-step explanation:

Let us solve it now.

y = x² - 18

Take -18 to the left side

y + 18 = x²

Now remove the square of x

√y + 18 = x

Consider two unique parallel lines. What aspects of
these two lines are the same? What aspects of these two
lines would have to be different? Explain your reasoning.

Answers

Answer:

The slope of two parallel lines will always be the same. If the slope was slightly different, then the lines would intersect at some point, which breaks the definition of parallel lines.

The y-intercepts of two parallel lines have to be different, or else the two lines would be the same line. If the y-intercept and the slope are the same, then the lines will essentially equal each other.

Answer:

Sample Response: Two parallel lines will have the same slope. The slopes of parallel lines have to be equal. The y-intercepts of those two lines have to be different, otherwise they would be the same line. The x-intercepts of the parallel lines would also be different.

Step-by-step explanation:

edge 2020

What is the inverse of the given function f(x)=1/4x -12?

Answers

Answer:

  [tex]f^{-1}(x)=4x+48[/tex]

Step-by-step explanation:

To find the inverse, solve for y:

  x = f(y)

  x = (1/4)y -12

  x +12 = (1/4)y . . . . add 12

  4(x +12) = y . . . . . multiply by 4

  y = 4x +48 . . . . . . simplify

The inverse function is ...

  [tex]\boxed{f^{-1}(x)=4x+48}[/tex]

A survey was sent out to compare the proportion of adults who use their car horns when driving for two age populations (1=younger adults, defined as between 20 and 39 years old and 2 =older adults, defined as over 60 years old). The following data was obtained from those who responded.

Calculate the 90% confidence interval using the standard normal distribution. Note that 1 =0.52. P2= 0.35, and s.e.(P1-P2) =0.0338. Round to the fourth decimal point. Please enter you answer in the following format: (lower value, upper value)

Use the horn Use the horn
Group Yes No Total
1= younger adults 261 240 501
2= older adults 123 229 352

Answers

Answer:

The  90% confidence interval for the difference between proportions is (0.115, 0.228).

As the value 0 is not included in the interval, we can conclude that there is significant difference in the proportion of youger adults that use the horn and older adults that use the horn.

Step-by-step explanation:

We want to calculate the bounds of a 90% confidence interval.

For a 90% CI, the critical value for z is z=1.645.

The sample 1 (younger adults) , of size n1=501 has a proportion of p1=0.521.

[tex]p_1=X_1/n_1=261/501=0.5210[/tex]

The sample 2 (older  adults), of size n2=352 has a proportion of p2=0.3494.

[tex]p_2=X_2/n_2=123/352=0.3494[/tex]

The difference between proportions is (p1-p2)=0.1715.

[tex]p_d=p_1-p_2=0.5210-0.3494=0.1715[/tex]

The pooled proportion, needed to calculate the standard error, is:

[tex]p=\dfrac{X_1+X_2}{n_1+n_2}=\dfrac{261+123}{501+352}=\dfrac{384}{853}=0.4502[/tex]

The estimated standard error of the difference between means is computed using the formula:

[tex]s_{p1-p2}=\sqrt{\dfrac{p(1-p)}{n_1}+\dfrac{p(1-p)}{n_2}}=\sqrt{\dfrac{0.4502*0.5498}{501}+\dfrac{0.4502*0.5498}{352}}\\\\\\s_{p1-p2}=\sqrt{0.0005+0.0007}=\sqrt{0.0012}=0.0346[/tex]

Then, the margin of error is:

[tex]MOE=z \cdot s_{p1-p2}=1.645\cdot 0.0346=0.0569[/tex]

Then, the lower and upper bounds of the confidence interval are:

[tex]LL=(p_1-p_2)-z\cdot s_{p1-p2} = 0.1715-0.0569=0.115\\\\UL=(p_1-p_2)+z\cdot s_{p1-p2}= 0.1715+0.0569=0.228[/tex]

The  90% confidence interval for the difference between proportions is (0.115, 0.228).

The sum of a number and twenty-one is sixty-four.

Answers

Answer:

43

Step-by-step explanation:

If X + 21 = 64

then subtract 64 by 21 and you get 43

43 is the answer I believe

What is the slope of the line given by the equation below?
y-20 = 5(x-2)

Answers

Answer:

5

Step-by-step explanation:

first you need to simplify this equation and put it in slope intercept form which is y = mx + b

after simplifying you will get y = 5x + 10

since the slope is m , the answer will be 5

Please help. I keep getting this problem wrong . I need help please . I’ll mark you as brainliest if correct . Only answer if you know. Thank you

Answers

Answer:

The real number 'a' = 32

The real number 'b' = 0

Step-by-step explanation:

Product of a number of a number and its conjugate = a + bi

The number is = -4 + 4i

Conjugate of this number is = -4 - 4i

Product of the number and it's conjugate

= (-4 + 4i)(-4 - 4i)

= -4(-4 - 4i) + 4i(-4 - 4i) [By distributive property]

= 16 + 16i - 16i - 16i²

= 16 - 16(-1)

= 16 + 16

= 32

a + bi = 32 + (0)i

By comparing both the sides,

a = 32

b = 0

Joana wants to buy a car. Her parents loan her $5,000 for 5 years at 5% simple interest. How much will Joana pay in interest?

Answers

Answer:

1250

Step-by-step explanation:

5% of $5000 is 250

250X5= 1250

Which explains why the graph is not a function?

Answers

Answer:

56

Step-by-step explanation:

Type your answers into the boxes.
There are 36 students in a class. The pie chart shows the colour of their hair.
Students' Hair Colours
40°
Red
Blonde
Dark
240°
How many students have blonde hair?
How many students have dark hair?
How many students have red hair?

Answers

Answer:

(a)24

(b)8

(c)4

Step-by-step explanation:

Number of STudents in the Class = 36

Angle representing Students with Red Hair =40 degrees

Angle representing Students with Blonde Hair =240 degrees

Therefore:

(a)Number of Students with Blonde Hair

[tex]=\dfrac{240^\circ}{360^\circ} \times 36\\\\ =24$ students[/tex]

(b)Number of Students with Dark Hair

Angle representing students with dark hair = 360-(240+40)=80 degrees

Therefore:

Number of Students with Dark Hair

[tex]=\dfrac{80^\circ}{360^\circ} \times 36\\\\ =8$ students[/tex]

(c)Number of Students with Blonde Hair

[tex]=\dfrac{40^\circ}{360^\circ} \times 36\\\\ =4$ students[/tex]

There are 8 students that have blond hair

There are 24 students that have dark hair

There are 4 students that have red hair

Please find attached the pie chart used in answering this question

A pie chart is a graph that displays information in a circle. The circle is divided into slices which represent a numerical proportion. The sum of angles in a pie chart is 360 degrees

To determine the number of students with a type of hair, use this formula :

(degree of the slice that represents the hair type / 360) x total number of students in the class

Degree of the slice that represents blond hair = 360 - (240 + 40) = 80

Students that have blonde hair = [tex]\frac{80}{360}[/tex]  x 36 = 8

Students that have dark hair = [tex]\frac{240}{360}[/tex] x 36 = 24

Students that have red hair = [tex]\frac{40}{360}[/tex] x 36 = 4

To learn more about pie charts, please check : https://brainly.com/question/11433309?referrer=searchResults

f(x)=x^3+10x^2-25x-250

Answers

Answer:

-16x^5

Step-by-step explanation:

f(x)=x^3+10x^2-25x-250

f(x) = x^3-15x+x^2-250

f(x) = x^5-15x-250

f(x) = x^5 -x + 16

f(x) = -x^5+16

f(x) = -16x^5

// have a great day //

A random sample of adult female reaction times has a sample mean of x¯=394.3 milliseconds and sample standard deviation of s=84.6 milliseconds. Use the Empirical Rule to determine the approximate percentage of adult female reaction times that lie between 140.5 and 648.1 milliseconds.

Answers

Answer:

The percentage of adult female reaction times that lie between 140.5 and 648.1 milliseconds is 99.7%.

Step-by-step explanation:

The Empirical Rule states that, for a normally distributed random variable:

68% of the measures are within 1 standard deviation of the mean.

95% of the measures are within 2 standard deviation of the mean.

99.7% of the measures are within 3 standard deviations of the mean.

In this problem, we have that:

Mean = 394.3 ms

Standard deviation = 84.6 ms

Use the Empirical Rule to determine the approximate percentage of adult female reaction times that lie between 140.5 and 648.1 milliseconds.

140.5 = 394.3 - 3*84.6

So 140.5 is 3 standard deviations below the mean.

648.1 = 394.3 + 3*84.6

So 648.1 is 3 standard deviations above the mean.

By the Empirical Rule,

The percentage of adult female reaction times that lie between 140.5 and 648.1 milliseconds is 99.7%.

Trapezoid ABCD is graphed in a coordinate plane,
What is the area of the trapezoid?
4
3
B
С
16 square units
O 24 square units
32 square units
48 square units
-5 4 3 2 -11
1 2 3 4 5 x
-5

Answers

Answer:

24 square units

Step-by-step explanation:

The formula for computing the area of a trapezoid is shown below:

As we know that

Area of a trapezium is

[tex]= \frac{1}{2} \times h(a+b)[/tex]

where

h = perpendicular height

The a and b =  length of the parallel sides.

Now,

h = 2 - -2 = 4 units

a = 5 - -3 = 8 units

b = 3 - -1 = 4 units

Now placing these values to the above formula

So, the area of a trapezoid is

[tex]= \dfrac{1}{2} \times 4(8+4)[/tex]

[tex]= 2 \times 12[/tex]

= 24 square units.

Hence we applied the above formula so that the area of trapezoid could come

Any help would be great

Answers

Answer:

88/57

Step-by-step explanation:

Answer: 88:57

Step-by-step explanation:

Length is 88 and width is 57

So the ratio is 88:57

A tree that is 10 feet tall is growing at a rate of 2 foot each year. A tree that is 14 feet tall is growing at a rate of 2/3 foot each year. What is the number of years it will take for both trees to be the same height, and what will their height be?

Answers

Answer:

after three years

Step-by-step explanation:

Eleanor can drive an average of 374 Miles on one tank of gas. How many miles can she drive on 15 tanks of gas

Answers

Answer:

5,610 Miles

Step-by-step explanation:

To solve this you would need to multiply the average miles by how many tanks of gas she will use.

374 * 15 = 5,610

So, Eleanor can drive 5,610 miles with 15 tanks of gas.

i need help asap!!!!!

Answers

Answer:

31 degrees

Step-by-step explanation:

Since RPS and QPR make up QPS, the sum of their angle measures must be 47. Therefore:

3x-38+7x-95=47

10x-133=47

10x=180

x=18

QPR=7(18)-95=126-95=31

Hope this helps!

write eight hundred and seven thousand, two hundred and five in figures

Answers

Answer:

807,205

Step-by-step explanation:

Take the eight hundred and seven thousand and express that has 807,000. Then, add the two hundred and five at the end to get 807,205

The given statement is written in figures 807,205.

The given statement is eight hundred and seven thousand, two hundred and five in figures.

We need to write the given statement as the number.

What are numbers?

A number is a mathematical object used to count, measure, and label. The original examples are the natural numbers 1, 2, 3, 4, and so forth. Numbers can be represented in language with number words.

Now, eight hundred and seven thousand, two hundred and five=807,205.

Therefore, the given statement is written in figures 807,205.

To learn more about the numbers visit:

https://brainly.com/question/17429689.

#SPJ2

8. A biotech company is looking for a user experience researcher to organize and report on some user experience data for a health and wellness app. They need to know the demographics of the users and the average time the app is open for each demographic. In the technical interview, you are asked to describe your approach to the initial analysis. When describing your analysis plan for the request, with what type of statistics would you tell the interviewer you would start your analysis

Answers

Answer:

Descriptive statistics

Step-by-step explanation:

Descriptive statistics describes and summarizes the basic features of a given dataset. It explains features from a collection of information, it is also said to be a form of summary statistics. Here data is characterized using its properties.

In this case, I was asked to describe my approach to the initial analysis. When describing the analysis plan for the request, I would tell the interviewer to start analysis using descriptive statistics.

convert 6 kilograms to grams

Answers

Answer:

6000 grams the formula would be multiply the mass value by 1000

Step-by-step explanation:

Answer:

6000 grams

Step-by-step explanation:

6 kilograms

To convert kg into grams, we multiply by 1000

So,

=> 6 * 1000 grams

=> 6000 grams

Please answer this correctly

Answers

Answer:

0-4: Make it 2 units tall

5-9: Make it 5 units tall

10-14: Make it 1 unit tall

15-19: Make it 4 units tall

20-24: Make it 4 units tall

Step-by-step explanation:

0-4: 2, 2 (2 numbers)

5-9: 6, 7, 7, 8, 9 (5 numbers)

10-14: 14 (1 number)

15-19: 15, 16, 16, 18 (4 numbers)

20-24: 21, 23, 23, 24 (4 numbers)

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