6. Suppose that (W, Z) have a bivariate normal distribution, that W~N(0, 1), and that the...
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....
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?
6. Suppose W and Z have a bivariate normal distribution 1 2(1-2 (-2pzw+w2) fzw(z, w) 27T Find the distribution of the RV E(Z|W). Explain your derivation. [12] 6. Suppose W and Z have a bivariate normal distribution 1 2(1-2 (-2pzw+w2) fzw(z, w) 27T Find the distribution of the RV E(Z|W). Explain your derivation. [12]
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...
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?
the conditional distribution of Z, given that W-sN(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:...
bos on 559 2. Random variable X and Y have a bivariate normal distribution. The conditional density of X given Y = y is a OVH a. bivariate normal distribution Bossiu b. chi-square distribution c. linear distribution oms d. normal distribution e. not necessarily any of the above distributions. 3. The probability distribution for the random variable X is shown by the table. Use the transformation technique to construct the table for the probability distribution of Y = x2 +...
Suppose (X, Y ) has bivariate normal distribution, E(X) = E(Y ) = 0,V ar(X) = σX2 , V ar(Y ) = σY2 and Correl(X, Y ) = ρ. Calculate the conditional expectation E(X2|Y ). I. Suppose (X,Y) has bivariate normal distribution, E(X) = E(Y) 0, Var(X)-σ , Var(Y) σ and Correl (X,Y)-p. Calculate the conditional expectation ECKY expectation E(X2Y)