Stats question (1 Viewer)

[acmilan]

I got this question in the quiz and its been annoying me since i guessed the answer.

It went something like:

If P(X = k) = e^-33^k/k! find E(X-1)²

Anyone know how to do it? I tried expanding but it got really ugly and figured it was better to use my time on the other questions and guess that one.

 

[SeDaTeD]

Oh green sheet? I got that one too, I just guessed that one also, which I found out later to be the right guess .
Well E(X-1)^2 = E(X^2) - 2E(X) + 1.
E(X) is lambda which is 3
for E(X^2) = Sum from 1 to inf of (e^-3*3^k/k!)*k^2
=SUM 3e^-3*k(3^(k-1)/(k-1)!)
=SUM 3e^-3*k(x^(k-1)/(k-1)!) , at x=3
=SUM 3e^-3*d/dx[x^k/(k-1)!]
=sum from 1 to inf of 3e^-3*d/dx[x*x^(k-1)/(k-1)!]
=3e^-3*d/dx[x*e^x]
=3e^-3*(e^x + xe^x)
=3e^-3*(e^3 + 3e^3) at x=3
=3(1+3)
=12

then E(X-1)^2 = E(X^2) - 2E(X) + 1
= 12 - 2*3 +1 =7

i know, giant pain in the arse. Actually one of the guys pointed out that variance of a poisson distribution was also lambda (whihc can be proved along similar lines).

var(X) = E(X^2) - (E(X))^2 = lambda = 3
E(X^2) - (E(X))^2 + (E(X))^2 - 2E(X) + 1 = 3 + (E(X))^2 -2E(X) + 1 = 3 + 9 -6 + 1 = 7
E(X-1)^2 = 7

Are you in my tute btw?

 

[acmilan]

Thanks!

If you're in the Friday @ 11am tute then I am in there.

 

[SeDaTeD]

Yep that's the one. Did you guess right btw?

 

[acmilan]

Nope i said 9

 

[Templar]

Oh well, better than my guess of none of the choices.