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Answer: Geometric Distribution: Mean and Variance In
Chapter 4, Problem 27E(choose chapter or problem)
Geometric Distribution: Mean and Variance In Exercise, use the fact that the mean of a geometric distribution is \(\mu=1 / p\) and the variance is \(\sigma 2=q / p 2\).
Daily Lottery A daily number lottery chooses three balls numbered 0 to 9. The probability of winning the lottery is 1/1000. 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 $500. Would you expect to make or lose money playing this lottery? Explain.
Questions & Answers
QUESTION:
Geometric Distribution: Mean and Variance In Exercise, use the fact that the mean of a geometric distribution is \(\mu=1 / p\) and the variance is \(\sigma 2=q / p 2\).
Daily Lottery A daily number lottery chooses three balls numbered 0 to 9. The probability of winning the lottery is 1/1000. 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 $500. Would you expect to make or lose money playing this lottery? Explain.
ANSWER:Step 1 of 4
The geometric distribution is a discrete probability distribution that models the likelihood of success occurring after a certain number of failures in a sequence of independent Bernoulli trials. A Bernoulli trial is an experiment with two possible outcomes: success or failure, with a constant probability of success, p, on each trial.