Suppose that X and Y have the following joint probability density function. f(x,y) = 134² 0 < x < 5, y > 0, x − 2 < y < x+2 (a) Find E(XY). (b) Find the covariance between X and Y.

Let X denote 0.025 × the ambient air temperature (˚C) and let Y denote the time (min) that it takes for a diesel engine to warm up. Assume that (X, Y) has joint probability density function f(x,y) = 1.6x (1 − x)(6 + 5x − 4y), for 0 < x < 1, 0 < y < 0.5. While you cannot guess the value of the correlation from the regression curve for X or Y, do they suggest whether it likely is positive or negative?

2. Let the joint probability density function of continuous random variables X and Y be given by Find fx|y(x|y). f(x, y) = 2 if 0 < x < y < 1 elsewhere.