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?
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.
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...
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.