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  3. a an exponential random variable x has probability densityuntion pdx...

Question: a an exponential random variable x has probability densityuntion pdx...

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a) An exponential random variable X has probability densityuntion: pdx]- forx20 Give a formula for the generating function of X b) A Beta random variable X has probability density function: pdfx] 6(1-x)x for0SxSI Give a formula for the generating function of X. (Tip: You can calculate: by first caleulatinge dx and differentiating with respect to t twice L.4) The generating function for the sum of independent random variables a) Given two independent random variables, X1 with generating function GX1[t] and X2 with generating function GX2[t], how do you get the generating function of X1 + X2? b) Given three independent random variables, Xl with generating function GX1[t]. X2 with generating function GX2t] and X3 with generating function GX3t], how do you get the generating function of X1 X2+ X3?

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