Recent content by hellokitten

Given P(A), P(B), and P(A n B) . Find the P(A' n B' | A') We know P(AuB) = P(A)+P(B)- P(A n B) Then P(A' n B'|A') = P(A' n B' n A' ) / P(A') = P(A' n B') / P(A') = P(A u B)' /P(A') = [1-P(A u B) ]/ P(A') = [1-P(A u B)] / [1-P(A)] Correct?

Nevermind. I got it! Thanks!

Why does having k as an eigenvalue of S automatically mean that the rank of S-KI < 4?

K,a,b,c is not identically zero then det(S) =/= 0 => S is full rank. The question stated to verify that the rank of S-I*lamda = 3. This is needed to prove the geometric multiplicity. of lamda =1.

Oh Sorry! X can be any number. a,b,c are non zero numbers.

Let S = [ x x x x ; a x x x ; 0 b x x ; 0 0 c x] Find the rank of S-K*identity. Attempt I basically did straight forward row reduction and got [ (x-k) x x x ; 0 ((x-k)^2-ax)/(x-k) x-ax/(1-k) a- ax/(1-k); 0 0 (x-k)-b[x(x-k)-ax]/ [(x-k)^2-ax]...

Homework Statement IF G, H and G+H are invertible matrices and have the same dimensions Prove that G(G^-1 + H^-1)H(G+H)^-1 = I 3. Attempt G(G^-1 +H^-1)(G+H)H^-1 = G(G^-1G +G^-1H + H^-1G + H^-1H)H^-1 = (GG^-1GH^-1 +GG^-1HH^-1 +GH^-1GH^-1 +GH^-1HH^-1) = GH^-1+I +GH^-1GH^-1 +GH^-1 =2GH^-1+...

Homework Statement Let x be an exponential random variable with lamda = .5 P(x=5|2<x<9} = 0 since exponential is continuous => probability of any single number = 0 Calculate E[x| 2<x<9] = integral from 2 to 9 of (x* .5*exp(-.5*x)) dx ? is this true or is there something wrong because of the...

Oh. It assumes no covariance.

Homework Statement Find the variance of Y=3x^2+3x+3The Attempt at a Solution Let Y = 3x^2 +3x +3 Var(Y) = Var(3x^2 +3x +3) = 9Var(x^2) +9Var(x) = 9 [E[X^4] - E[X^2]^2 +E[X^2] - E[X]^2] This is wrong.