# Solve the following problem : If X follows Poisson distribution with parameter m such that P(X=x+1)P(X=x)=2x+1 Find mean and variance of X. - Mathematics and Statistics

Sum

Solve the following problem :

If X follows Poisson distribution with parameter m such that
("P"("X" = x + 1))/("P"("X" = x)) = (2)/(x + 1)
Find mean and variance of X.

#### Solution

Given, X ~ P(m) and ("P"("X" = x + 1))/("P"("X" = x)) = (2)/(x + 1)

The p.m.f. of X is given by

P(X = x) = ("e"^(-"m")"m"^x)/(x!)

∴ According to the given condition, we get

(("e"^(-"m")"m"^(x + 1))/((x + 1)!))/(("e"^(-"m")"m"^x)/(x!)) = (2)/(x + 1)

∴ ("e"^(-"m") xx "m"^x xx "m")/((x + 1) xx x!) xx (x!)/("e"^(-"m") xx "m"^x) = (2)/(x + 1)

∴ "m"/(x + 1) = (2)/(x + 1)

∴ m = 2
∴ Mean = Variance = m = 2.

Concept: Poisson Distribution
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#### APPEARS IN

Balbharati Mathematics and Statistics 2 (Commerce) 12th Standard HSC Maharashtra State Board
Chapter 8 Probability Distributions
Part II | Q 1.14 | Page 157