Suppose that X and Y have the following joint probability distribution: f(x, y) 4 0.15 0.10 3 0.20 0.30 5 0.10 0.15 Determine whether the two random variables are dependent or independent.

The joint probability distribution function of X and Y is given by: 1 2 3 1 0.05 0.06 0.10 X 2 0.13 0.21 0.30 a. Find the conditional distribution of Y given X = 1 b. Find the conditional distribution of X given Y = 2 5 0.02 0.03 0.10

The joint probability distribution of two random variables X, Y is given in the table below. Y=-4 Y=0 Y=1_Y=4 X=-4 0.01 0.18 0.00 0.13 X=-1 0.03 0.08 0.20 0.14 X=4 0.00 0.08 0.09 0.06 From the information in the table, calculate each of the following three probabilities. (a) P(Y= -4) = | (b) Р (х < -1, ү 2 0) %3D0 (c) P(x< 5) = []

Let discrete random variables X and Y have the following probability distribution: Y 1 -1 0.10 0.18 0.10 X 0.09 0.15 0.23 1 0.03 0.05 0.07 Find the E(X2 Y²) -0.91 1.18 0.91 1.0494