# Homework Help: Multivariate normal distribution , conditional probability problem

1. Jun 28, 2012

### wuid

1. The problem statement, all variables and given/known data
Given X,Y RV both have normal distribution with:
$μ_{x}=6$,$μ_{y}=4$,$σ_{x}=1$,$σ_{y}=5$,ρ=0.1

a. are X,Y independent?
b. find P(X≤5)
c. find P(Y≤5|X=5)

2. The attempt at a solution

a. no -> ρ=0.1 -> cov(X,Y)≠0

b. define Z=$\frac{X-6}{1}$ ; Z~N(0,1)
so P(X≤5) = P(Z≤-1) = $\Phi(-1)$

c. Here i have my difficulty were i able to calculate and i know :
μ=[6 4] , Ʃ=[1 0.5,0.5 25] cov matrix , $Ʃ^{-1}$= [$\frac{100}{99} \frac{-2}{99}, \frac{-2}{99} \frac{4}{99}$] inverse matrix.

just don't how to deal with the conditional question...