Problem 5: A professor tries to count the number of students attending lecture in person. For each student in the audience, the professor either counts the student accurately with probability p or misses the student in the count with probability (1 – p). The exact number of attending students is 20. (a) The number of students counted by the professor is a random variable N. What is the PMF of N?
Problem 5: A professor tries to count the number of students attending lecture in person. For each student in the audience, the professor either counts the student accurately with probability p or misses the student in the count with probability (1 – p). The exact number of attending students is 20. (a) The number of students counted by the professor is a random variable N. What is the PMF of N?
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![Problem 5: A professor tries to count the number of students attending
lecture in person. For each student in the audience, the professor either
counts the student accurately with probability p or misses the student in the
count with probability (1 – p). The exact number of attending students is
20.
(a) The number of students counted by the professor is a random variable
N. What is the PMF of N?
(b) Let U = 20 – N denote the number of uncounted students. What is the
PMF of U?
(c) What is the probability that the undercount U is 2 or more?
(d) For what value of p is E[U] = 2?](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fbbfc8250-1df3-458c-8274-8bf80d6812bf%2Fce4f23c4-5693-4ccd-a416-b463ed788fd8%2F22nhb_processed.png&w=3840&q=75)
Transcribed Image Text:Problem 5: A professor tries to count the number of students attending
lecture in person. For each student in the audience, the professor either
counts the student accurately with probability p or misses the student in the
count with probability (1 – p). The exact number of attending students is
20.
(a) The number of students counted by the professor is a random variable
N. What is the PMF of N?
(b) Let U = 20 – N denote the number of uncounted students. What is the
PMF of U?
(c) What is the probability that the undercount U is 2 or more?
(d) For what value of p is E[U] = 2?
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