Q3. Suppose that X and Y are random variables denoting the fraction of a day that...

Transcribed Image Text:

Q3. Suppose that X and Y are random variables denoting the fraction of a day that a request for merchandise occurs and the receipt of shipment occurs, respectively. The joint probability density function is 0<x<1, 0<y<1, |0, 1, f(x, y) = otherwise. a) What is the probability that both the request for merchandise and receipt of an order occur during the first half of the day? b) What is the probability that a request for merchandise occurs after its receipt? Before its receipt. c) Determine the correlation coefficient between X and Y. Comment on the correlation coefficient. d) Determine the CDF, F(x,y) of the above probability function. e) Determine P(0<x<.4, 0.5<y<1). Q3. Suppose that X and Y are random variables denoting the fraction of a day that a request for merchandise occurs and the receipt of shipment occurs, respectively. The joint probability density function is 0<x<1, 0<y<1, |0, 1, f(x, y) = otherwise. a) What is the probability that both the request for merchandise and receipt of an order occur during the first half of the day? b) What is the probability that a request for merchandise occurs after its receipt? Before its receipt. c) Determine the correlation coefficient between X and Y. Comment on the correlation coefficient. d) Determine the CDF, F(x,y) of the above probability function. e) Determine P(0<x<.4, 0.5<y<1).