Suppose {Yn; n 1} is a sequence of independent, identically distributed Bernoulli random variables with...

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Suppose {Yn; n ≥ 1} is a sequence of independent, identically distributed Bernoulli random variables with Pr {Y₁ = 1}=p, and Pr {Y₂ = 0} = 1-p where 0 < p < 1. Let X be a Poisson random variable with parameter x > 0, and, also, independent of {Yn; n ≥ 1}. Define (a) Find the distribution of U. (b) Find the distribution of V. X U=Yk, and V=X - U. k=1 Suppose {Yn; n ≥ 1} is a sequence of independent, identically distributed Bernoulli random variables with Pr {Y₁ = 1}=p, and Pr {Y₂ = 0} = 1-p where 0 < p < 1. Let X be a Poisson random variable with parameter x > 0, and, also, independent of {Yn; n ≥ 1}. Define (a) Find the distribution of U. (b) Find the distribution of V. X U=Yk, and V=X - U. k=1

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