A joint random variable (X1, X2) is said to have a bivariate normal distribution if its joint density is given by

for €“ˆž (a) Show that E(X1) = μX1 and E(X2) = σX2.
(b) Show that variance (X1) = σ2X1, variance (X2) = σ2X2, and the correlation coefficient is
(c) Show that marginal distributions of X1 and X2 are normal.
(d) Show that the conditional distribution of X1, given X2 = x2, is normal with mean

and variance σ2x1(1 €“ p2).

Transcribed Image Text:

fx1.x2 (s, t) = 2) Tx Tx Tx σχ