Hello,Can someone please solve problem 3?Thanks ## Problem 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?*---## Problem 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 $?

Given that a trial has just resulted in a hung jury because 8 numbers of the jury were in favor of a…

3. A trial has just resulted in a hung jury because eight numbers 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 EX and SD(X). (c) What is the pmf and cdf of Y = 3 - X?

3. A trial has just resulted in a hung jury because eight numbers 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 EX and SD(X). (c) What is the pmf and cdf of Y = 3 - X?

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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Question

Hello,

Can someone please solve problem 3?

Thanks

## Problem 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?*

---

## Problem 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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