2. Show that a. P.(-x) =(-1)*P(x) b. Px.(0) - (-1) 2(!) c. P(0) - 0 3....
Question 3 Using (P)(1-P) P 0<P <1 Evaluate the following integral 4 dy • 1+ Solution
Let X N(1,3) and Y~ N(2,4), where X and Y are independent 1. P(X <4)-? P(Y < 1) =? 4、 5, P(Y < 6) =? 7, P(X + Y < 4) =?
0, P - 0 2 ) - 1. 3. Let (X, A,) be a complete measure space. Assume that A, B E A with (A) = (B) < . Show that if A CCCB, then CE A. 4 Let A and Rhe two collections of euheete of Y Aceume that any cot in 4 halanes
Provided N(0, 1) and without using the LSND program, find P( - 2 <3 <0) Provided N(0, 1) and without using the LSND program, find P(Z < 2). Provided N(0, 1) and without using the LSND program, find P(Z <OOR Z > 2). Message instructor about this question Provided N(0, 1) and without using the LSND program, find P(-1<2<3). 0.84 Message instructor about this question
let a,b > 0 . Prove that DI < Val
2. Suppose P and Q are positive odd integers such that (PQ)-1. Prove that Qm] Pn] P-1 0-1 0<m<P/2 0<n
2. Let Px(x) = 1, X = 1,2,3, 4, 5, zero elsewhere, be the pmf of X. Find P(X = 1 or 2), P(3 < X < ), and P(1 < X < 2).
2. (5) Solve each of the following 2) (r+7)?(x-3); <0 b) 2x +3r-11x 26
Write down the elements of the following: • A = {x + Z: c2 < 2}, 4. P(P(A1-{-1})),
is independent of X, and e Problem 3 Suppose X N(0, 1 -2) -1 <p< 1. (1) Explain that the conditional distribution [Y|X = x] ~N(px, 1 - p2) (2) Calculate the joint density f(x, y) (3) Calculate E(Y) and Var(Y) (4) Calculate Cov(X, Y) N(0, 1), and Y = pX + €, where