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- Assume that the probability that an airplane engine will fail during a torture test is 12and that the aircraft in question has 4 engines. Construct a sample space for the torture test. Use S for survive and F for fail.Find the probability of each event. Getting 2 red eggs in a single scoop from a bucket containing 5 red eggs and 7 yellow eggsLet X and Y be random variables having the same distribution. Show that Cov(X +Y, X – Y) = 0.
- Suppose that the random variables X and Y are independent with Var(X)=8 and Var(Y)=6. Calculate Var(5X−7Y+17)Show that if X, Y are independent random variables, then Cov(X, Y ) = 0.Let X1, X2,... , Xn be independent Exp(A) random variables. Let Y = X(1)min{X1, X2, ... , Xn}. Show that Y follows Exp(nA) dis- tribution. Hint: Find the pdf of Y
- The 4-dimensional random vector X has PDF fX(x)={1 when 0≤xi≤1, i=1,2,3,4 and 0 otherwise}. Are the for components of X independent random variables?Let X and Y be independent discrete random variables and suppose that X+Y=2. Show that X and Y are constant random variables.Let X1 and X2 be discrete random variables with joint probability distribution x1 = 1, 2; x2 = 1, 2, 3, f(x1, x2) = 10, 18 elsewhere. Find the probability distribution of the random variable Y = X1X2.
