SOLUTION: Let 𝑌 have a Poisson distribution with mean 𝜆. Show 𝐸[𝑌 (𝑌 − 1)] = 𝜆
2
and 𝑉(𝑌 ) = 𝜆
Algebra.Com
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) (Show Source): You can put this solution on YOUR website!
The proof for if Y is the Poission distribution can be found in many standard texts in probability and statistics, and even in the internet.
We show .
,
since and for the Poisson distribution.
RELATED QUESTIONS
Given that x has a poisson distribution with (mean) u=7, what is the probability that... (answered by Edwin McCravy)
Given that x has a poisson distribution with (mean) u=0.38, what is the probability that... (answered by ewatrrr)
(a) Find the mean and variance of the random variable X having the following probability (answered by robertb)
The military historian, Von Bortkewitsch, obtained the following data on the number of... (answered by reviewermath)
let x have a normal distribution with mean of 24 and standard deviation of 6 find the... (answered by ewatrrr)
Banner Mattress and Furniture Company wishes to study the number of credit applications... (answered by jim_thompson5910)
A random variable has a Poisson distribution such that P(X = 1) = P(X = 2).
Compute:
(answered by Boreal)
If the number of flaws on a piece of plywood occurs randomly and follows the Poisson... (answered by Boreal)
Given that has a Poisson distribution with u=3, what is the probability that... (answered by Positive_EV)