Let X and Y distributed random variables representing voltages measured in volts at two different nodes of a circuit. X has the marginal density function.

You are also given the conditional density function.

(a) Compute P (Y ? 0.5| x = 0.5) the probability that Y is less than or equal to 0.5 that we X = 0.5.

(b) Compute he probability that the voltage X is in the range ? ? X ? ? at the same time. In other words compute the probability P (? ? X ? ?, Y ?1/2).

x(x) = {2+, 0251, 1o. otherwise fy (y|x) = 2, 0x1 and 0 y 1, 2(x+y) 0. otherwise