• A2 Let the joint distribution of X and Y be given by the following two-way table: Y-1 -1b 0 0 1 a X 0 1 0 a 1-2a-2b 0

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A2 Let The Joint Distribution Of X And Y Be Given By The Following Two Way Table Y 1 1b 0 0 1 A X 0 1 0 A 1 2a 2b 0 1 (54.71 KiB) Viewed 30 times

• A2 Let the joint distribution of X and Y be given by the following two-way table: Y-1 -1b 0 0 1 a X 0 1 0 a 1-2a-2b 0 0 b [3] Here, a, b are unknown constants such that the above table is a valid two-way table. For parts (a)-(d) you may leave your results in terms of a and b where necessary. (a) Compute the marginal pmfs px and py. [3] (b) Compute E[X] and E[Y]. (c) Compute Var(X) and Var(Y). [3] (d) Compute Corr(X,Y) in the case (a,b) + (0,0). (5) (e) What constraints must the pair (a, b) satisfy to ensure that the table above is valid? [2] (f) What is the smallest value Corr(X,Y) can take in this case? Give a value of (a, b) for which the smallest possible value of Corr(X,Y) is attained. [2]