Step 1

From the provided information, the marginal probability distribution of both the random variables X and Y are given.

Since both the variables are independent, the condition probability distribution of Y given X is equal to the marginal probability distribution of Y that is,

\(P(Y|X)=P(Y)\)

\(=f_{y}(y), 0\leq y \leq 1\)

Step 2

The required probability can be calculated as:

\(P(Y|X>2)=P(Y>2)=0\)

Thus, the probability is 0 because the range of Y is from 0 to 1 only.