Let X be the number of H that we obtain by flipping a fair coin 3 times and Y is the number of H that we obtain by flipping a not fair coin with p(H) = 4 times. a) Find the probability mass functions and the distribution functions of X and Y. b) Are X + Y and X.Y independent? Explain why or why not. c) Compute the expectation, the variance and the standard deviation of 2X + XY. d) Compute the covariance and the correlation of X and Y.

Let X be the number of H that we obtain by flipping a fair coin 3 times and Y is the number of H that we obtain by flipping a not fair coin with p(H) = 4 times. a) Find the probability mass functions and the distribution functions of X and Y. b) Are X + Y and X.Y independent? Explain why or why not. c) Compute the expectation, the variance and the standard deviation of 2X + XY. d) Compute the covariance and the correlation of X and Y.

College Algebra (MindTap Course List)

12th Edition

ISBN:9781305652231

Author:R. David Gustafson, Jeff Hughes

Publisher:R. David Gustafson, Jeff Hughes

Chapter8: Sequences, Series, And Probability

Section8.7: Probability

Problem 39E: Assume that the probability that an airplane engine will fail during a torture test is 12and that...

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