1. You are studying for the final exam of a math course. The professor has given you 30 proofs to know for the exam and they plan to ask you about six (6) of the proofs, chosen at random, on the exam. Suppose that you understand and can perfectly recreate 23 of the 30 proofs. If any of the remaining seven (7) proofs appear on the exam, you will not attempt to answer them. To answer this question, first define an appropriate random variable and identify its probability distribution and relevant parameter values. (a) What is the probability you will correctly state all six (6) proofs? (b) If you can correctly state at least four (4) of the proofs, what is the probability you can correctly state all six (6) proofs?
1. You are studying for the final exam of a math course. The professor has given you 30 proofs to know for the exam and they plan to ask you about six (6) of the proofs, chosen at random, on the exam. Suppose that you understand and can perfectly recreate 23 of the 30 proofs. If any of the remaining seven (7) proofs appear on the exam, you will not attempt to answer them. To answer this question, first define an appropriate random variable and identify its probability distribution and relevant parameter values. (a) What is the probability you will correctly state all six (6) proofs? (b) If you can correctly state at least four (4) of the proofs, what is the probability you can correctly state all six (6) proofs?
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
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Problem 1P
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![of a math course. The professor has given you 30 proofs to know for
1. You are studying for the
the and they plan to ask you about six (6) of the proofs, chosen at random, on the. Suppose that
you understand and can perfectly recreate 23 of the 30 proofs. If any of the remaining seven (7) proofs
appear on the , you will not attempt to answer them. To answer this question, first define an appropriate
random variable and identify its probability distribution and relevant parameter values.
(a) What is the probability you will correctly state all six (6) proofs?
(b) If you can correctly state at least four (4) of the proofs, what is the probability you can correctly state all
six (6) proofs?
2. Suppose that the probability distribution of a discrete random variable Y can be described by the formula
p(y) = k(2y-3)', y = 1, 2, 3, 4.
(a) What is the value of k?
(b) Compute (i) E(Y), (ii) V(Y), (iii) E(Y² – 1), and (iv) E
Y +1
3. A communication system consists of n components, each of which will, independently, function with
probability p.
(a) Let X, denote the number of components working in an n-component system. What is the probability
distribution of X,?
(b) The total system will be able to operate effectively if at least one-half of its components function. For
what values of p is a 5-component system more likely to operate effectively than a 3-component system?
4. For a nonnegative integer-valued random variable Y, show that LiP(Y >i) =HE(Y*)= E(Y)].
-0
5. During the month of May, the number of calls received by the ITS Service Desk at Carleton University
follows a Poisson distribution with a mean of 5 calls per hour. To answer each of the following questions,
first define an appropriate random variable and identify its probability distribution and relevant parameter
values.
(a) What is the probability that more than two calls are received in a one-hour period?
(b) What is the probability that exactly ten calls are received during a two-hour period?
(c) If the ITS staff take a 30-minute break for lunch, what is the probability that they do not miss any calls?
(d) Refer to part (c). What is the probability that the ITS staff do not miss any calls during lunch on at least
three out five days?](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F717c41c9-7610-4369-a9d8-d14d52c86513%2F81a1a7e5-c480-45b3-8e7f-8dd0831cca24%2Flxe0oi3_processed.jpeg&w=3840&q=75)
Transcribed Image Text:of a math course. The professor has given you 30 proofs to know for
1. You are studying for the
the and they plan to ask you about six (6) of the proofs, chosen at random, on the. Suppose that
you understand and can perfectly recreate 23 of the 30 proofs. If any of the remaining seven (7) proofs
appear on the , you will not attempt to answer them. To answer this question, first define an appropriate
random variable and identify its probability distribution and relevant parameter values.
(a) What is the probability you will correctly state all six (6) proofs?
(b) If you can correctly state at least four (4) of the proofs, what is the probability you can correctly state all
six (6) proofs?
2. Suppose that the probability distribution of a discrete random variable Y can be described by the formula
p(y) = k(2y-3)', y = 1, 2, 3, 4.
(a) What is the value of k?
(b) Compute (i) E(Y), (ii) V(Y), (iii) E(Y² – 1), and (iv) E
Y +1
3. A communication system consists of n components, each of which will, independently, function with
probability p.
(a) Let X, denote the number of components working in an n-component system. What is the probability
distribution of X,?
(b) The total system will be able to operate effectively if at least one-half of its components function. For
what values of p is a 5-component system more likely to operate effectively than a 3-component system?
4. For a nonnegative integer-valued random variable Y, show that LiP(Y >i) =HE(Y*)= E(Y)].
-0
5. During the month of May, the number of calls received by the ITS Service Desk at Carleton University
follows a Poisson distribution with a mean of 5 calls per hour. To answer each of the following questions,
first define an appropriate random variable and identify its probability distribution and relevant parameter
values.
(a) What is the probability that more than two calls are received in a one-hour period?
(b) What is the probability that exactly ten calls are received during a two-hour period?
(c) If the ITS staff take a 30-minute break for lunch, what is the probability that they do not miss any calls?
(d) Refer to part (c). What is the probability that the ITS staff do not miss any calls during lunch on at least
three out five days?
Transcribed Image Text:1. You are studying for the final exam of a math course. The professor has given you 30 proofs to know for
the exam and they plan to ask you about six (6) of the proofs, chosen at random, on the exam. Suppose that
you understand and can perfectly recreate 23 of the 30 proofs. If any of the remaining seven (7) proofs
appear on the exam, you will not attempt to answer them. To answer this question, first define an appropriate
random variable and identify its probability distribution and relevant parameter values.
(a) What is the probability you will correctly state all six (6) proofs?
(b) If you can correctly state at least four (4) of the proofs, what is the probability you can correctly state all
six (6) proofs?
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