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6. Suppose W and Z have a bivariate normal distribution 1 2(1-2 (-2pzw+w2) fzw(z, w) 27T...
8. Suppose W and Z have a bivariate normal distribution 1 1 2(1-p2) (-2pzw+u2) fzw (z, w) 27T 1 (i) Find the marginal density of W then compute its MGF Mw and use it to find the mean and the variance of W. [3 (ii Find fzw (z|w) and use it to identify the distribution of Z given W = w aW bwhere a, b E R. [2 (iii) Derive the density of Y (iv) Compute the mean and variance...
6. Suppose that (W, Z) have a bivariate normal distribution, that W ∼ N (0, 1), and that the conditional distribution of Z, given that W = w, is N (aw + b, τ 2 ). (a) What is the marginal distribution of Z? (b) What is the conditional distribution of W, given that Z = z? 6. Suppose that (W, Z) have a bivariate normal distribution, that W N(0,1), and that the conditional distribution of Z, given that W-w....
6. Suppose that (W, Z) have a bivariate normal distribution, that W~N(0, 1), and that the conditional distribution of Z, given that W-w, is N(aw b, T2). (a) What is the marginal distribution of Z? b) What is the conditional distribution of W, given that Z-2?
Suppose that (W,Z) have a bivariate normal distribution, that W ~N(0,1), and that the conditional distribution of Z, given that Ww, is N(aw b,T2). (a) What is the marginal distribution of Z? (b) What is the conditional distribution of W, given that Z2?
The random variables Z and W have a bivariate normal dis- tribution with EZ] = E[W] = 0, Var(Z) = Var(W) = 1, and oorrelation ρ E (-1,1). Given that Pl2+ W 1-8413, find the value ofp. Hint: 8413 = φ(1), where φ is the standard normal distribution function.] The random variables Z and W have a bivariate normal dis- tribution with EZ] = E[W] = 0, Var(Z) = Var(W) = 1, and oorrelation ρ E (-1,1). Given that Pl2+...
6. Suppose that X and Y have a bivariate normal distribution with px 1 and y- (a) Order the following probabilities from largest to smallest, assuming p >0: P(X 2 (b) Repeat (a) assuming p < 0. (c) Repeat (a) assuming we are interested in (X 0.25) instead of (x 2 2). 6. Suppose that X and Y have a bivariate normal distribution with px 1 and y- (a) Order the following probabilities from largest to smallest, assuming p >0:...
3-5.2. Let X, Y, and Z have the joint pdf 3/2 1 |ryz exp exp 27T 2 where -o<x < o,-00< y < oo, and 00< z < 00. While X, Y, and Z are obviously dependent, show that X, Y, and Z are pairwise independent and that each pair has a bivariate normal distribution 3-5.2. Let X, Y, and Z have the joint pdf 3/2 1 |ryz exp exp 27T 2 where -o
Question 2 15 pts Suppose that X and Y form a bivariate normal distribution. You are given that E[X] = E[Y] = 0, with o x = 3, oy - 2. Further, the correlation between X and Y is 0.5. Find P(X<Y +1). Upload Choose a File
please help me 6. Suppose X, Y have a bivariate normal distribution with marginal dis- tribution X ~ N(0,1) and the conditional distribution of Y given X-x is N(ax + b,a?). (i). What is the marginal distribution of Y? (ii). What is the conditional dist ribut ion of X given Y-y?
Suppose that X and Y form a bivariate normal distribution. You are given that E[X] = E[Y] = 0, with o x = 3, 0y = 2. Further, the correlation between X and Y is 0.5. Find P(X<Y + 1).