Let X and Y be two jointly distributed continuous random variables representing

Question

Let X and Y be two jointly distributed continuous 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 Compute P(Y 0.5|X = 0.5) the probability that Y is less than or equal to 0.5 given that we know X = 0.5. Compute the probability that the voltage X is in the range 1/4 X 1/2 and the voltage Y is less than 1/2 at the same time. In other words compute the probability P(1/4 X 1/2, Y 1/2). Compute the covariance of X and Y.

Explanation / Answer

(f_{Y}(y|0.5)=2(y+0.5)/2=y+0.5 P(Y<=0.5|X=0.5)=int_{0}^{0.5}(y+0.5)dy=0.375)

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