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Answer to Question #31661 in Statistics and Probability for Vlatko

Question #31661
I have a couple of questions for function and Sample mean and CLT. Any question for any of the questions and I'll be grateful!

III. Functions of two random variables, Sample mean, CLT.
1. Let X and Y be independent r.v.’s such that X is uniform r.v over (2,3), and Y is uniform r.v over (1,4).
1.1 Find and sketch the pdf of Z = X + Y.
2. Find
3. 3.1 Consider two r.v.’s X and Y with joint . Determine the pdf of Z = XY.
3.2 Let X and Y be independent such that X is uniform r.v over (0,2), and Y is uniform r.v over (1,3). Find the pdf of Z = XY.

3. Ten independent samples of a random variable X are taken. Determine the expected value and variance of the sample mean if the r. v X is uniformly distributed over (-1,1).
4. A certain component is critical to the operation of an electrical system and must be replaced immediately upon failu
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