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- Suppose that y(x1,x2) = x1/x2, where x1 and x2 are two independent random variables. Which of the following equations is CORRECT?If X, Y are standardized random variables and r(aX+bY,bX+aY)= 1+2ab a²+b² I Find r(X,Y), coefficient of correlation between X and Y.Let X1, X2, ..., X, be independent random variables and Y = min{X1, X2, ..., Xm}. Fy (y) = 1 – || (1 – Fx,(y)) i=1 (a) A certain electronic device uses 5 batteries, with each battery to have a life that is exponentially distributed with mean of 48 hours and is independent of the life of other batteries. If the device fails as soon as at least one of its batteries fail, what is the expected life of the device?
- Suppose that X₁, X₂, X3 are mutually independent random variables with the respective moment generating functions, Mx, (t) = e²²², Mx₂ (t) = e²t + 3t², and Mx₂(t) = (-¹)². State with parameter(s) the probability distribution of Y = X₁ + X₂.Suppose that X and Y are random variables where the conditional expected value of Y given X is given by E(Y|X)= 4X²+2X+3 If X~Po(1) is a poisson variable with the parameter A = 3 determine the expected value E(Y) of Y.If a random variable X has the moment generating function Mx (t)= 2 - ť Determine the variance of X.
- Suppose that X and Y are independent random variables with finite variances such that E(X) = E(Y). Show that: E[(X-Y)2] =Var(X) +Var(Y)Suppose that X and Y are random variables with E(XY) = E(X)E(Y). Then X and Y * independent. Also Var(X + Y) = Var(X) + Var(Y) true.If X and Y are independent random variables with E(X) = 10, Var(X) = 4, E(Y) = 12 and VAR(Y) = 3, If W =-2X +Y Find E(W) and STD (W) (a) (b) If X and Y are not independent, with E(X) =10, VAR(X) = 5, E(I) =18, VAR(Y) = 3 and CovX,Y) = -2. If W = X – 2Y Find E(W) and STD(W)
- Suppose that X and Y are independent random variables with EX=EY=100, and E[min(X,Y))=79. Find ElX-Y|, (the mean of the absolute value of X-Y).Let X and Y be two random variables with E (X) = 1, E (Y) = 2, Var (X) = 1, Var (Y) = 2, !! Cov (X, Y) = 0.5. For what values of a and b such that the random variable aX + bY have mean 3 and variance 4 ?1) If Var(X- Y) = 2, Var(X+ Y) = 4, E(X) = 3 and E(Y) = 1, than what is E(XY)? 2) IfX and Y are independent random variables with, E(X)%30%3D E(Y), show that Var(XY) Var(X) x Var(Y). %3D
