6. Show that Var[X] = E[X2], if EX] = 0.
Suppose that EX-EY-0, var(X) = var(Y) = 1, and corr(X,Y) = 0.5. (i) Compute E3X -2Y]; and (ii) var(3X - 2Y) (ii) Compute E[X2]
(2. Assume that X, Y, and Z are random variables, with EX) = 2, Var(X) = 4, E(Y) = -1, Var(Y) = 6, E(Z) = 4, Var(Z) = 8,Cov(X,Y) = 1, Cov(X, Z) = -1, Cov(Y,Z) = 0 Find E(3X + 4y - 62) and Var(3x + 4y - 62).
From this density How will get following EX, var(X), M(t). Please proof that in details f(x)= 1 exp(-T) We were unable to transcribe this image
How do you rearrange this equation to isolate t. Show your work. ln[A]t =−kt+ln[A]0
If g(x)=−ln(1−x) , what is g^(k)(0) (for k=1,2,3,… ) ?options:a) 1/kb)1/1-kc)k!d)(k-1)!e) (k+1)!
2. Lex X be uniformly distributed over (a ó). Show that EX- and Var(X) (bof using the first and second moments of this random variable where the pdf of X() Note that the nth moment (b-a) 12 EXj-ooox"f(x)dx of a continuous random variable is dehned aS
Assume X, Y are independent with EX = 1 EY = 2 Var(X) = 22 Var(Y) = 32 Let U = 2X + Y and V = 2X – Y. (a) Find E(U) and E(V). (b) Find Var(U) and Var(V). (c) Find Cov(U,V).
Given: eX - LN(x) = 4. If x = 0.05 is one solution for the equation, use a graphing calculator to find another solution. O 0.57 O 1.27 O 1.48 O 2.17 0 3.33
E(X) 2 and EX(X - 1))-5. Find Var(X)