Example 1.2: 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).
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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
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