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Question

If a random variable X has a Poisson distribution with mean 5, then the expectation

E[(X+2)2] equals.


  1. 54

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Solution

The correct option is A 54
  1. case of poisson distribution

    Mean = Variance = 5 (given)

    Variance (x)=E(x2)E2 (x)

    5=E(x2)(5)2

    E(x2)=30

    So, E(x+2)2=E[x2+4x+4)

    =E(x2)+4E(x)+4

    = 30 + 4 × 5 + 4 = 54

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