- #1

wuid

- 40

- 0

## Homework Statement

Given X,Y RV both have normal distribution with:

[itex]μ_{x}=6[/itex],[itex]μ_{y}=4[/itex],[itex]σ_{x}=1[/itex],[itex]σ_{y}=5[/itex],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=[itex]\frac{X-6}{1}[/itex] ; Z~N(0,1)

so P(X≤5) = P(Z≤-1) = [itex]\Phi(-1)[/itex]

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 , [itex]Ʃ^{-1}[/itex]= [[itex]\frac{100}{99} \frac{-2}{99}, \frac{-2}{99} \frac{4}{99}[/itex]] inverse matrix.

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