Consider a Gaussian random variable, X , with mean µ and variance σ2. The random variable is transformed by the device whose input– output relationship is shown in the accompanying figure. Find and sketch the PDF of the transformed random variable, Y.
Answer to relevant QuestionsLet X be a Gaussian random variable with zero mean and arbitrary variance, σ2. Given the transformation Y= X3, find fY (y). Let X be a Chi- square random variable with a PDF given by Where c= n/ 2 for any positive integer n. Find the PDF of Y= √X. Two discrete random variables have a joint PMF as described in the following table. (a) Find the marginal PDFs, PM (m) and PN (n). (b) Find (N = 1|M =2). (c) Find (M = N). (d) Find (M > N). A pair of random variables has a joint PDF specified by (a) Find the marginal PDFs, fX (x) and fY(Y). (b) Based on the results of part (a), find E [X], E [y], Var (X), and Var (Y). (c) Find the conditional PDF, f X|Y ...Consider again the joint CDF given exercise 5.3. (a) For constants a and b, such that 0 < a < 1, 0 < b < 1 and a < b, find Pr (a < X < b). (b) For constants and, such that, 0 < c < 1, 0 < d < 1 and c < d, find Pr (c < y < ...
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