(a Recalling the definition of 2 for a single rv X, write a formula that would b

Question

(a Recalling the definition of 2 for a single rv X, write a formula that would be appropriate for computing the variance of a function h(X y Remember that variance is just a special expected value. of two random variables. Hint: E(h(X, Y) (b) An instructor has given a short quiz consisting of two parts. For a randomly selected student, let X the number of points earned on the first part and Y the number of points earned on the second part. Suppose that the joint pmf of X and Y is given in the accompanying table. p(x, y) 0 5 10 15 0 0.03 0.06 0.02 0.10 x 5 0.04 0.14 0.20 0.10 10 0.01 0.15 0.14 0.01 Use the formula from part (a) to compute the variance of the recorded score h(x, n l- max(X, Y)] if the maximum of the two scores is recorded. (Round your answer to two decimal places.)

Explanation / Answer

from above given table :

adding above cell wise calculation E(max(X,Y) =9.55

also

therefore adding above cell wise calculation E(max(X,Y)2) =105.25

hence V(max(X,Y) =E(max(X,Y)2)-(E(max(X,Y))2 =105.25-9.552 =14.0475

please revert .

E(max(X,Y)) =P(X,y)*Max(x,y) 0 0.3 0.2 1.5 0.2 0.7 2 1.5 0.1 1.5 1.4 0.15

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