If two random variables X and Y are statistically independent, then X and Y are said to be uncorrelated. That is, (1) Ryy = E[X Y]= E[X]E[Y] %3D
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- If a game gives payoffs of $10 and $100 with probabilities 0.9 and 0.1, respectively, then the expected value of this game is E=0.9+0.1= .(TRUE / FALSE) For two random variables, X and Y , E(XY ) = E(X)E(Y ) if X and Y are uncorrelated.If X and Y are independent Poisson random variables with E[X] = 3 and E[Y] = 2, what is P[ X = 2 | X + Y = 4 ]?
- Suppose X and Y are the random variables with joint PMF given by: X/Y 11.2 5.75 -3 0 0.07 -2 0.2 0.08 -1 0.1 0.1 0 0.15 0.1 1 0 0.2 a.) Compute E(X2)Consider the following joint random variable pmf for X and Y: x y -1 0 1/4 0 1 1/8 1 1 1/2 1 0 1/8 What is the correlation of X and Y?If Y is a discrete random variable with possible values of 1, 2, and 4, and the probability mass function is given by P(Y = 1) = 0.2, P(Y = 2) = 0.5, and P(Y = 4) = 0.3, what is the variance of Y?