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.

Only need (b), thank you

Suppose that  X and Y  have the following joint probability density function.f (x, y)  =  3x 400      0  <  x  <  6,  y  >  0,  x − 4  <  y  <  x + 4 (a) Find E(XY). (b) Find the covariance between X and Y.

Suppose that the random variables X and Y have the following joint probability density function. f(x, y) = ce-6x-2y, 0 < y < x. (a) Find the value of c. (b) Find P(X < Y < 2) ,

[1] The joint probability density function of two continuous random variables X and Y is sc, 0

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.

Suppose that X and Y have a joint probability density function given by Sce-32-5y if r, y 2 0 fx.x(r, y) = otherwise (a) Determine the value of the normalization constant c. (b) Find the marginal probability density function fx and state the name of the distribution of X. (c) Find the conditional probability density function fy|x=z•

1. Consider the two functions ƒ(x) = C(2x − x³), g(x) = C(2x − x²), 0 < x < 2. (1) Could f be a probability density function? If so, determine C. If not, explain the reason that why f is not a probability density function. 0 < x < 2, (2) Could g be a probability density function? If so, determine C. If not, explain the reason that why g is not a probability density function.

Let X be a random variable with probability density function [ a + bx², 0