4. Define a discrete random variable by the probability mass function Pr(X= k) = A(0.99) ² for some constant A, and k ≥ 0. Do the following in a Jupyter note- book. You should include either text blocks or code comments describ- ing what you are doing and clearly stating answers to the questions. (a) Use Python code to find an approximation of the constant A required to make this into a valid probability distribution. This amounts to finding the value of an infinite series, make sure your answer is accurate to at least 4 decimal places. (b) Calculate E[X] and Var(X) for this distribution. (c) Produce a bar plot of the probability mass function over a rea- sonable domain.
4. Define a discrete random variable by the probability mass function Pr(X= k) = A(0.99) ² for some constant A, and k ≥ 0. Do the following in a Jupyter note- book. You should include either text blocks or code comments describ- ing what you are doing and clearly stating answers to the questions. (a) Use Python code to find an approximation of the constant A required to make this into a valid probability distribution. This amounts to finding the value of an infinite series, make sure your answer is accurate to at least 4 decimal places. (b) Calculate E[X] and Var(X) for this distribution. (c) Produce a bar plot of the probability mass function over a rea- sonable domain.
Computer Networking: A Top-Down Approach (7th Edition)
7th Edition
ISBN:9780133594140
Author:James Kurose, Keith Ross
Publisher:James Kurose, Keith Ross
Chapter1: Computer Networks And The Internet
Section: Chapter Questions
Problem R1RQ: What is the difference between a host and an end system? List several different types of end...
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![4. Define a discrete random variable by the probability mass function
Pr(X = k) = A(0.99)k²
for some constant A, and k ≥ 0. Do the following in a Jupyter note-
book. You should include either text blocks or code comments describ-
ing what you are doing and clearly stating answers to the questions.
(a) Use Python code to find an approximation of the constant A
required to make this into a valid probability distribution. This
amounts to finding the value of an infinite series, make sure your
answer is accurate to at least 4 decimal places.
(b) Calculate E[X] and Var(X) for this distribution.
(c) Produce a bar plot of the probability mass function over a rea-
sonable domain.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F3cafa2c1-a76b-449e-9796-7de6b3b95bcc%2Ffa858d38-1935-4c78-aa31-a4ec60dd5f10%2F82e8q1k_processed.png&w=3840&q=75)
Transcribed Image Text:4. Define a discrete random variable by the probability mass function
Pr(X = k) = A(0.99)k²
for some constant A, and k ≥ 0. Do the following in a Jupyter note-
book. You should include either text blocks or code comments describ-
ing what you are doing and clearly stating answers to the questions.
(a) Use Python code to find an approximation of the constant A
required to make this into a valid probability distribution. This
amounts to finding the value of an infinite series, make sure your
answer is accurate to at least 4 decimal places.
(b) Calculate E[X] and Var(X) for this distribution.
(c) Produce a bar plot of the probability mass function over a rea-
sonable domain.
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