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2. It was reported that 7 in 10 auto accidents involve a single vehicle. Let X be the number of accidents that involved a single vehicle among 3 randomly selected accidents. (a) Find the pmf function of X. (b) What is the cumulative distribution function of X? Tabulate the pmf function and the cdf of X? (c) What are the expected value and standard deviation of X?

2. It was reported that 7 in 10 auto accidents involve a single vehicle. Let X be the number of accidents that involved a single vehicle among 3 randomly selected accidents. (a) Find the pmf function of X. (b) What is the cumulative distribution function of X? Tabulate the pmf function and the cdf of X? (c) What are the expected value and standard deviation of X?

A First Course in Probability (10th Edition)
A First Course in Probability (10th Edition)
10th Edition
ISBN:9780134753119
Author:Sheldon Ross
Publisher:Sheldon Ross
Chapter1: Combinatorial Analysis
Section: Chapter Questions
Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...
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**Exercise 2** It was reported that 7 in 10 auto accidents involve a single vehicle. Let \( X \) be the number of accidents that involved a single vehicle among 3 randomly selected accidents. - **(a)** Find the pmf (probability mass function) of \( X \). - **(b)** What is the cumulative distribution function (cdf) of \( X \)? Tabulate the pmf function and the cdf of \( X \). - **(c)** What are the expected value and standard deviation of \( X \)? *(Hint: Note that \( X \) is the number of accidents that involve a single vehicle among 3 accidents. What distribution is it?)* **Exercise 3** A trial has just resulted in a hung jury because eight members of the jury were in favor of a guilty verdict and the other four were for acquittal. Suppose the jurors leave the jury room in random order and each of the first three leaving the room is accosted by a reporter in quest of an interview. - **(a)** What is the pmf of \( X = \) the number of jurors favoring acquittal among those interviewed? - **(b)** Find \( E(X) \) and \( SD(X) \). - **(c)** What is the pmf and cdf of \( Y = 3 - X \)?
Transcribed Image Text:**Exercise 2** It was reported that 7 in 10 auto accidents involve a single vehicle. Let \( X \) be the number of accidents that involved a single vehicle among 3 randomly selected accidents. - **(a)** Find the pmf (probability mass function) of \( X \). - **(b)** What is the cumulative distribution function (cdf) of \( X \)? Tabulate the pmf function and the cdf of \( X \). - **(c)** What are the expected value and standard deviation of \( X \)? *(Hint: Note that \( X \) is the number of accidents that involve a single vehicle among 3 accidents. What distribution is it?)* **Exercise 3** A trial has just resulted in a hung jury because eight members of the jury were in favor of a guilty verdict and the other four were for acquittal. Suppose the jurors leave the jury room in random order and each of the first three leaving the room is accosted by a reporter in quest of an interview. - **(a)** What is the pmf of \( X = \) the number of jurors favoring acquittal among those interviewed? - **(b)** Find \( E(X) \) and \( SD(X) \). - **(c)** What is the pmf and cdf of \( Y = 3 - X \)?
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