GATE EC 2016 Set A Question no 2

GATE EC 2016 Set A Question no 2


The second moment of a Poisson distributed random variable is 2. The mean of the random variable is _________.
Solution
We know that if λ is parameter of Poisson’s Distribution
Then,
    First moment = λ
    Second moment = λ * λ + λ
    Given that Second moment = 2
    We have λ * λ + λ = 2
    λ * λ + λ – 2 = 0
   (λ  -1 )(λ  + 2) = 0
   λ  = – 2 or λ = 1
   As λ  cannot be equal to – 2 hence λ  = 1 is the Answer.
Hence, First Moment = 1
Answer = 1