Question

For the joint probability distribution f(x,y)=xy, where =0,1,2,3x=0,1,2,3 and =3y=3, find-

A) P(X≤2,Y=1)
B) P(X>2,Y≤1)
C) P(X>Y)
D) P(X=Y=4)

Answer 1

The question addresses calculating probabilities from a joint discrete probability distribution via multiplication and summation of the given function values. P(X ≤ 2, Y = 1) would require summing probabilities for valid X and Y pairs, while P(X = Y = 4) equals zero since 4 is outside the provided domain of X and Y.

Step-by-step explanation:

The question involves finding probabilities from a joint probability distribution for discrete random variables X and Y. To calculate these probabilities, one needs to consider the values of X and Y provided, multiply these values as per the given function f(x, y) = xy, and then sum up probabilities as per each case asked in the question (A, B, C, D).

For example, the probability P(X ≤ 2, Y = 1) involves finding probabilities for all pairs where X is 0, 1, or 2 and Y is 1, then summing these individual probabilities.

However, it is worth noting that the last part, P(X = Y = 4), is not possible given the domain provided, as the maximum value for X and Y is 3. Therefore, P(X = Y = 4) = 0.