Problem 7. The table below shows the joint probability distribution of the random variables X and Y. Joint probability distribution 10 08 05 16 15 12 09 14 Answer the following questions (show your calculations): 1. Are the two requirements satisfied for this bivariate probability distribution? Explain clearly. 2. Find the marginal probability distribution of X and graph it. Find the mean and standard deviation of X. 3. Find the marginal probability distribution of Y and graph it. Find the mean and standard deviation of Y. 4. Find the correlation coefficient between X and Y. Comment on the direction and the strength of the association between X and Y. 5. Find the conditional probability distribution of X given that Y = 3 and graph it. 6. Find the conditional mean E(X|Y=3) and the conditional variance V(X|Y=3).
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Are the two requirements satisfied for this bivariate probability distribution? The two requirements for a bivariate probability distribution are: a) All probabilities must be non-negative: P(X, Y) ≥ 0 for all X and Y. b) The sum of all probabilities must equal Show more…
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