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Thread: Exponential and Poisson Distribution Problem

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    Exponential and Poisson Distribution Problem




    Hello all, we have this problem.

    Suppose that the continuous random variable T has the Exponential distribution with expected value 4. Given that T = t, for any t > 0, the discrete random variable S has the Poisson distribution with expected value 3t.
    Find:
    a) E(S)
    b) Var(S)

    Can you help me out with this one? I struggle to find the answer, but i know its relatively easy .. Thank you.

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    Re: Exponential and Poisson Distribution Problem

    I don't have emotions and sometimes that makes me very sad.

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    Re: Exponential and Poisson Distribution Problem


    We know that T~Expo(λ) => Ε(Τ) = 1/λ so we can derive that λ = 1/4
    We also know that S~Poi(λ) => λ here is the expected value, so λ = 3t = 3T

    Somewhere here i get stuck..

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