Use the fact that the mean of a geometric distribution is μ=1/p and the variance is σ2 =q/p2 A daily number lottery chooses two balls numbered 0 to 9. The probability of winning the lottery is 1/100. Let x be the number of times you play the lottery before winning the first time. (a) Find the mean, variance, and standard deviation. (b) How many times would you expect to have to play the lottery before winning? It costs $1 to play and winners are paid $300. Would you expect to make or lose money playing this lottery? Explain.

Question
Asked Oct 19, 2019
144 views

Use the fact that the mean of a geometric distribution is μ=1/p and the variance is σ=q/p

A daily number lottery chooses two balls numbered 0 to 9. The probability of winning the lottery is 1/100. Let x be the number of times you play the lottery before winning the first time. 

(a) Find the mean, variance, and standard deviation. (b) How many times would you expect to have to play the lottery before winning? It costs $1 to play and winners are paid $300. Would you expect to make or lose money playing this lottery? Explain. 

check_circle

Expert Answer

Step 1

It is given that x is the number of times to play the lottery before winning first time.

 p = 1/100 and q = 99/100.

a).

The mean is calculated as follows.

fullscreen
Step 2

The variance and standard deviation calculated as follows.

help_outline

Image Transcriptionclose

99 100 1 100 99 -x100 100 2-9,900 O99.5

fullscreen
Step 3

b). from part (a), the expected number of lotteries to play to get first win is 100.

Therefore, the expected ...

help_outline

Image Transcriptionclose

Expected value of the game expected win - expected lose - 300 -1 100 =2

fullscreen

Want to see the full answer?

See Solution

Check out a sample Q&A here.

Want to see this answer and more?

Solutions are written by subject experts who are available 24/7. Questions are typically answered within 1 hour.*

See Solution
*Response times may vary by subject and question.
Tagged in

Math

Statistics

Other

Related Statistics Q&A

Find answers to questions asked by student like you
Show more Q&A
add
question_answer

Q: In Problems 19-22, determine whether or not the histogram indicates that a normal distribution could...

A: 21. From the given histogram, the bars represents the relative frequencies for the lengths of the ph...

question_answer

Q: I lost my notes for solving this sample question for an upcoming exam. Some help reviewing would be ...

A: The total number of board of directors = 10.The officers need to be appointed = 3 (chief Executive o...

question_answer

Q: Esmeralda buys a bag of cookies that contains 5 chocolate chip cookies, 8 peanut butter cookies, 5 s...

A: It is given that a bag contains 5 chocolate chip cookies, 8 peanut butter cookies, 5 sugar cookies a...

question_answer

Q: An advertising executive wants to estimate the mean amount of time that consumers spend with digital...

A: a) The sample size is 117 and it is obtained below: From the given information, the population stand...

question_answer

Q: The Downitawn Parking Authority of Tampa, Florida, reported the following information for a sample o...

A: Hello. Since your question has multiple sub-parts, we will solve first three sub-parts for you. If y...

question_answer

Q: Hello, I am studying for an exam. I'm not sure how to tackle this problem and I cant find any exampl...

A: Consider a random variable X which, follows binomial distribution, indicates the number of couples w...

question_answer

Q: I lost my notes for solving this sample question for an upcoming exam. Some help reviewing would be ...

A: Part a)Probability that the person is female is 0.56.Calculations:

question_answer

Q: what is the power of each of the gollowing studies, using a t test for dependent means (based onthe ...

A: The conditions for the effect size for the t test means are:If d ≤ 0.2, then the effect size is smal...

question_answer

Q: Please see picture

A: It is given that the probabilities of answering 1st and 2nd questions are q1 and q2 respectively. An...