if for a poisson variate x, P(x=0)=P(x=1)=k, prove that k=1/e
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ANSWER
P(X=0)=0.1 and P(X=2)=0.2
P(0;μ)=
0!
e
−μ
μ
0
=e
−μ
= 0.1
P(2;μ)=
2!
e
−μ
μ
2
=0.2
=>
2
0.1μ
2
=0.2
=> μ =2
The parameter is mean (μ) in Poisson distribution, so = 2
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