If X and Y are two random variables, then the covariance is Cxy = Ryy – XY
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- 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 ]?(X³ , 2Y²-3Y+4) Calculate the covariance by creating a common distribution table for the given random variables (X,Y).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)
- (X³, 2Y²-3Y+4) Calculate the covariance by creating a common distribution table for the given random variables.If X1 and X2 are independent random variables with distribution given by P[Xi] = −1 = P[Xi = 1] = 1/2 for i = 1, 2, then are X1 and X1X2 independent?How do you show that if X1, X2,...Xn are independent random variables having the same Bernoulli distribution with the parameter θ and Y =X1 + X2 + ... + Xn, then E(Y) = nθ and var(Y) = nθ(1-θ)
- If the moment generating function of a random variable X is: (1/3+(2/3)e t ) 5 find P (X > 3).For two random variables X and Y where X∼ exponential(0.5) and Y|X = x ∼ N(5,x2), find E(E(X|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?