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- 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)Let P and Q be two independent Random variables with Var(P) = 5 and Var(Q) = 4. Find Var(7P+4Q-1).Suppose that the random variables X and Y are independent with Var(X)=8 and Var(Y)=6. Calculate Var(5X−7Y+17)
- Suppose that X is a N(3,4) random variable and suppose that Y=2X+1. Determine P(Y>8).Let X1 and X2 be two independent normal random variables with parameters (0,1) and (0,4) respectively. Let Y, = 2X, + X, and Y, = X, - 3X,. Find %3DSuppose that two random variables Y1 and Y, are independent, that is, for all values of y, and y2, P((Yı = y1) n (Y2 = y2)) = P(Y1 = y1)P(Y2 = y2) that is, the events (Yı = y1) and (Y2 = y2) are independent. Suppose also that Yı and Y, have the same Geometric distribution, that is Y1 random variable Y as the sum of Yı and Y2, that is, Y = Y1 +Y2. Geometric(p) and Ý2 ~ Geometric(p). Define a third
- Suppose X1, X2,.., Xn are independent random variables and each of them has a PMF Px(x) k forx = 1,2, 3, 4, 5 What is the value of k? What are the expected value and variance for each X;? What are the expected value and variance for X = E X;?3.Suppose that X and Y are independent random variables for which Var(X)=Var(Y)=3. Find the values of (a) Var(X-Y); (b) Var(2X-3Y+1).Let X1 , X2 , X3 be a collection of independent discrete random variables that all take the value 1 with probability p and take the value 0 with probability (1-p). The mean and variance of p-hat = 1/n ( X1 + X2 +... Xn ) . E(p-hat)= p Var(p-hat) = p(1-p) / n



