If x is a poisson variate such that 3p(x=4) = (1/2)p(x=2)+p(x=0), find mean of x and p(x<=2)
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Answered by
5
For Poisson's distribution, P(X) is given by
P(X)=
x!
e
−λ
.λ
x
It is given that P(X=2)=9P(X=4)+90P(X=6)
⇒
2!
e
−λ
.λ
2
=9.
4!
e
−λ
.λ
4
+90.
6!
e
−λ
.λ
6
Cancelling e
−λ
from both sides, we get
2!
λ
2
=9.
4!
λ
4
+90.
6!
λ
6
Since λ can not be zero, cancel out λ
2
from both sides to obtain
λ
4
+3λ
2
−4=0.
Solving , we get λ=1 as a valid solution.
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