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.
Algebra and Trigonometry (MindTap Course List)
4th Edition
ISBN:9781305071742
Author:James Stewart, Lothar Redlin, Saleem Watson
Publisher:James Stewart, Lothar Redlin, Saleem Watson
Chapter14: Counting And Probability
Section14.2: Probability
Problem 3E: The conditional probability of E given that F occurs is P(EF)=___________. So in rolling a die the...
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![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.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fce0afc3b-3e57-4487-b673-cf6f07e8890b%2Ff9cd4189-52c5-4aff-8598-24e2a9c9eb66%2Fopoudl_processed.jpeg&w=3840&q=75)
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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