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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&#039;ll be grateful!

III. Functions of two random variables, Sample mean, CLT.
1. Let X and Y be independent r.v.&rsquo;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.&rsquo;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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