4. + 3 points DevoreSta(95. E. 034 My Notes Ask Your Teacher (a) Recalling the d

Question

4. + 3 points DevoreSta(95. E. 034 My Notes Ask Your Teacher (a) Recalling the definition of a2 for a single rv X, write a formula that would be appropriate for computing the variance of a function hx Y) of two random variables. [Hint: Remember that variance is just a special expected value. - E(h(X, Y)P (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 0.01 0.06 0.02 0.10 x 50.04 0.16 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, y)ax(X, )] if the maximum of the two scores is recorded. (Round your answer to two decimal places.) Need Help?Read ItTalk to a Tutor

Explanation / Answer

(a) The values in the two blanks are y and x respectively.

(b) The various values of h (X,Y) and the respective probabilities are as shown in the below table:

The expected value of h(X,Y) = 9.65

V [max(X,Y)] = (0-9.65)2 x 0.01 + (5-9.65)2 x 0.06 + (10-9.65)2 x 0.02 + (15-9.65)2 x 0.1 + (5-9.65)2 x 0.04 + (5-9.65)2 x 0.16 + (10-9.65)2 x 0.2 + (15-9.65)2 x 0.1 + (10-9.65)2 x 0.01 + (10-9.65)2 x 0.15 + (10-9.65)2 x 0.14 + (15-9.65)2 x 0.01 = 12.6275

X,Y h(X,Y) p(X,Y) h(X,Y)*p(X,Y) 0,0 0 0.01 0 0,5 5 0.06 0.3 0,10 10 0.02 0.2 0,15 15 0.1 1.5 5,0 5 0.04 0.2 5,5 5 0.16 0.8 5,10 10 0.2 2 5,15 15 0.1 1.5 10,0 10 0.01 0.1 10,5 10 0.15 1.5 10,10 10 0.14 1.4 10,15 15 0.01 0.15

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