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4 Exercise Four: (25 pts) A professor tries to count the number of students attending lecture. For each student in the audience, the professor either counts the student properly (with probability $p$) or overlooks (and does not count) the student with probability $1 - p$. The exact number of attending students is 20. 1. The number of students counted by the professor is a random variable $N$. What is the PMF of $N$? 2. Let $U = 20 - N$ denote the number of uncounted students. What is the PMF of $U$? 3. What is the probability that the undercount $U$ is 2 or more? 4. For what value of $p$ does $E[U] = 1$?

          4 Exercise Four: (25 pts)
A professor tries to count the number of students attending lecture. For each student in the audience, the professor either
counts the student properly (with probability $p$) or overlooks (and does not count) the student with probability $1 - p$. The
exact number of attending students is 20.
1. The number of students counted by the professor is a random variable $N$. What is the PMF of $N$?
2. Let $U = 20 - N$ denote the number of uncounted students. What is the PMF of $U$?
3. What is the probability that the undercount $U$ is 2 or more?
4. For what value of $p$ does $E[U] = 1$?

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4 Exercise Four: (25 pts)
A professor tries to count the number of students attending lecture. For each student in the audience, the professor either
counts the student properly (with probability p) or overlooks (and does not count) the student with probability 1 - p. The
exact number of attending students is 20.
1. The number of students counted by the professor is a random variable N. What is the PMF of N?
2. Let U = 20 - N denote the number of uncounted students. What is the PMF of U?
3. What is the probability that the undercount U is 2 or more?
4. For what value of p does E[U] = 1?

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Elementary Statistics a Step by Step Approach

Allan G. Bluman 9th Edition

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Solved by Expert Dominador Tan

04/05/2023

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What is the PMF of N? The number of students counted by the professor can range from 0 to 20, as the professor can either count all the students or overlook all of them. Let's denote the number of students counted as n. The probability mass function (PMF) of N Show more…

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Exercise Four:(25 pts) A professor tries to count the number of students attending lecture. For each student in the audience, the professor either counts the student properly (with probability p) or overlooks (and does not count the student with probability 1 - p. The exact number of attending students is 20. 1. The number of students counted by the professor is a random variable N. What is the PMF of N? 2. Let U = 20 - N denote the number of uncounted students. What is the PMF of U? 3. What is the probability that the undercount U is 2 or more? 4. For what value of p does E[U] = 1?

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