Good morning every body

Please help me as soon as possible and thanks’ a lot

1-13: conditional probability density function (pdf) of the sum of two Gaussian random variables:

If x1 and x2 independent, the pdf of their sum x=x1+x2 conditional on x1 is

p(x\x1) = px2(x-x1) = N(x;x1+x-2, P22)

where: p([x1 x2]’) = N{ [x1 x2]’ ; [x-1 x-2]’, [ P11 P12;P21 P22]

Then, Find the pdf in general case?

1-14: probability matrix:

we have P{x (k) = xj\x (k-1) = xi} = πij i,j = 1, … , n

Find ∑j=1n (πij)