A fair coin is flipped three times. Let X represent the number of heads to occur on the first two flips and Y the number of heads to occur on the last two flips. (a) Find the joint probability function, along with each marginal function, for X and Y. b) Find cov(X, Y). c) Are X and Y independent? Explain your answer.
A fair coin is flipped three times. Let X represent the number of heads to occur on the first two flips and Y the number of heads to occur on the last two flips. (a) Find the joint probability function, along with each marginal function, for X and Y. b) Find cov(X, Y). c) Are X and Y independent? Explain your answer.
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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Transcribed Image Text:A fair coin is flipped three times. Let X represent the number of heads to occur
on the first two flips and Y the number of heads to occur on the last two flips.
(a) Find the joint probability function, along with each marginal function, for X and Y.
(b) Find cov(X, Y).
(c) Are X and Y independent? Explain your answer.
Hint: There are 8 outcomes for this expermient, e.g., if the outcome is HTT, then we have
X = 1 and Y = 0.
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