Question

If X is a Poisson variate such that 3P(X = 4) = 1/2P(X = 2) + P(X = 0). Find (1) the mean of X
(ii) P(X‹=2).​

Answer 1

Answer:

ANSWER

Poisson's distribution implies

P(X=n)=

n!

λ

n

e

−λ

Where mean=variance=λ

Hence P(x=2)=3P(x=3)

3

3!

λ

3

e

−λ

=

2!

λ

2

e

−λ

3λ=3

λ=1

Hence mean=variance=1