Let X and Y be uniformly distributed independent random variables on [0, 1]. a) Compute the...

Let X and Y be uniformly distributed independent random variables on [0, 1].
1. a) Compute the expected value E(XY ).
2. b) What is the probability density function fZ(z) of Z = XY ?
  Hint: First compute the cumulative distribution function FZ(z) = P(Z ≤ z) using a double integral, and then differentiate in z.
3. c) Use your answer to b) to compute E(Z). Compare it with your answer to a).

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orchestra answered 1 year ago

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