Multivariate normal distribution , conditional probability problem

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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...
 

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