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If a random variable X has a Poisson distribution with variance 6, then expectation [E(X + 3)2] equals _____.
    Correct answer is '87'. Can you explain this answer?
    Verified Answer
    If a random variable X has a Poisson distribution with variance 6, the...
    Var(X) = E(X) = 6
    Var(X) = E(X2) - (E(X))2
    6 = E(X2) – 36
    ∴ E(X2) = 42
    [E(X + 3)2]
    = E(X2 + 6X + 9 )
    = E(X2) + 6E(X) + 9         
    = 42 + 6× 6 + 9
    = 87  
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    If a random variable X has a Poisson distribution with variance 6, then expectation [E(X + 3)2] equals _____.Correct answer is '87'. Can you explain this answer?
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