Part f) compute the correlation between x and y The joint discrete density of in

Question

Part f) compute the correlation between x and y The joint discrete density of integer-valued random variables X and Y is given by y PX = x, Y = y] = Cy () (1/3)" (2/3)"-r for integers x, y: y = 1, 2, 3 and 0 i. Compute the value of the constantC a. By first summing over x for fixed y and then summing over y OR b. After carefully constructing the first table from the formula above w/o the constant C. Entries are proportional to probabilities. Then produce the (second) joint probability table blow. TOTAL Table 2: JOINT PROBABILITY TABLE TOTAL TOTAL ii. Compute the probability PIX+YS4]

Explanation / Answer

i.

ii

C x 1.592593 = 1

C=0.628

iii. for X+Y <= 4

iv

X Y 1 2 3 Total 1 0.333333 0.333333 2 0.444444 0.111111 0.555556 3 0.444444 0.222222 0.037037 0.703704 1.222222 0.333333 0.037037 1.592593

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