The continuous random variables X and Y are statistically independent and have marginal density functions fx(x) = 2x, 0 < x < 1, and fy(y) 1 y > 1. y2' Calculate the probability P(X < 0.5, Y < 2)

Consider two continuous random variables X and Y with joint pdf f(x,y)= 24x for 0

Suppose you have two independent random variables X ~ Y ~ Exponential(A2), A1 > 0, d2 > 0. Find: Exponential(A1) and (a) The joint density function for (X,Y). (b) P( > 1). (c) P(X +Y > 1).

Suppose that the amount of time a hospital patient must wait for a nurse's help is described by a continuous random variable with density function f(t) = e-t/3 where t≥ 0 is measured in minutes. (a) What is the probability that a patient must wait for more than 4 minutes? (b) A patient spends a week in the hospital and requests nurse assistance once each day. What is the probability that the nurse will take longer than 5 minutes to respond on (exactly) two occasions? (c) What is the probability that on at least one call out of seven, the nurse will take longer than 7 minutes to respond?