For two random variables X and Y, var(X + Y) = var(X)+ var(Y)+2 Cvy and var(X – Y) = var(X)+ var(Y)–2Cxy %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= .If a binomial experiment has probability p success, then the probability of failure is ____________________. The probability of getting exactly r successes in n trials of this experiment is C(_________, _________)p (1p)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)
- (TRUE / FALSE) For two random variables, X and Y, Var(X+Y) = Var(X)+Var(Y) if X and Y are uncorrelated.X and Y are random variables that are both Normally Distributed. The Mean of X is 5 and its SD is 3. The Mean of Y is -2 and its SD is 6. Find A and B, both greater than 0 so that P(4 < Y < 16) = P(A < X < B)You are given two random variables X and Y.E(X) = 0.5, Var(X) = 2E(Y) = 7, Var(Y) = 3.5cov (X, Y) = -0.8Find the variance of the random variable Z = 2X - 3Y
- A continuous random variable X is defined by: Solve: 1. f(x) = (3+x)²/16 ; -3≤ x≤ -1 2. f(x) = (6 - 2x)²/16 ; -1≤x≤1 3. f(x) = (3 - x²)/16 ; -1≤x≤3(TRUE / FALSE) For two random variables, X and Y , E(XY ) = E(X)E(Y ) if X and Y are uncorrelated.(X³ , 2Y²-3Y+4) Calculate the covariance by creating a common distribution table for the given random variables (X,Y).