 # If two random variables X and Y are independent with marginal pdfs fx(x)= 2x, 0\leq x \leq 1 and fy(y)=1,0\leq y \leq 1Calculate P(Y|X>2) midtlinjeg 2021-05-01 Answered

If two random variables X and Y are independent with marginal pdfs $$f_x(x)= 2x, 0\leq x \leq 1\ and\ f_y(y)=1,0\leq y \leq 1$$
Calculate $$P(Y|X>2)$$

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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.