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

• Jun 10th 2012, 02:44 AM
MathCrash
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: Attachment 24055) and U a random variable that takes values +/- 1 with probabilities 0.5 each. Find the pdf of Y=XU."

• Jun 11th 2012, 03:51 AM
SpringFan25
Re: Find the MGF of an r.v. that is a function of a continuous r.v. & a discrete r.v.
hint: $P(Y \leq k) = P(Y \leq k \cap U=-1) + P(Y \leq k \cap U=1)$
• Jun 11th 2012, 06:48 AM
HallsofIvy
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.