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Math Help - Find the MGF of an r.v. that is a function of a continuous r.v. & a discrete r.v.

  1. #1
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    Find the MGF of an r.v. that is a function of a continuous r.v. & a discrete r.v.

    I'm trolling through some old papers and this particular question has me stumped on how to solve - specifically I'm unsure how to proceed to derive the pdf of Y given that X is continuous while U is discrete.

    Q: "Let X be an exponential random variable (pdf: Find the MGF of an r.v. that is a function of a continuous r.v. & a discrete r.v.-codecogseqn-3-.png) and U a random variable that takes values +/- 1 with probabilities 0.5 each. Find the pdf of Y=XU."

    Advice gratefully received!
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  2. #2
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    Re: Find the MGF of an r.v. that is a function of a continuous r.v. & a discrete r.v.

    hint: P(Y \leq k) = P(Y \leq k \cap U=-1)  + P(Y \leq k \cap U=1)
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  3. #3
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    Re: Find the MGF of an r.v. that is a function of a continuous r.v. & a discrete r.v.

    You don't say it but I assume that the two random variables are independent.
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