SOLUTION: Let 𝑌 have a Poisson distribution with mean 𝜆. Show 𝐸[𝑌 (𝑌 − 1)] = 𝜆 2 and 𝑉(𝑌 ) = 𝜆

Algebra ->  Probability-and-statistics -> SOLUTION: Let 𝑌 have a Poisson distribution with mean 𝜆. Show 𝐸[𝑌 (𝑌 − 1)] = 𝜆 2 and 𝑉(𝑌 ) = 𝜆       Log On


   

Question 1184789: Let 𝑌 have a Poisson distribution with mean 𝜆. Show 𝐸[𝑌 (𝑌 − 1)] = 𝜆
2
and 𝑉(𝑌 ) = 𝜆
Answer by robertb(5830) About Me  (Show Source):
You can put this solution on YOUR website!
The proof for Var%28Y%29+=+lambda if Y is the Poission distribution can be found in many standard texts in probability and statistics, and even in the internet.

We show E%28Y%28Y-1%29%29+=+lambda.

,

since E%28Y%5E2%29+=+sigma%5E2+%2B+mu%5E2 and sigma%5E2+=+mu+=+lambda for the Poisson distribution.