# Question

An exponential random variable has a PDF given by fX(x) = exp (– x) u (x) .

(a) Find the mean and variance of X.

(b) Find the conditional mean and the conditional variance given that X > 1

(a) Find the mean and variance of X.

(b) Find the conditional mean and the conditional variance given that X > 1

## Answer to relevant Questions

A uniform random variable has a PDF given by fX (x) = u(x) – u (x – 1). (a) Find the mean and variance of X. (b) Find the conditional mean and the conditional variance given that 1 / 2 < X < 3 / 4. Let X be a standard normal random variable (i. e., X ~ N ( 0,1)). Find the PDF of Y= |X|. Let X be a Cauchy random variable whose PDF is given by Find the PDF of Y = 1 / 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 is uniformly distributed over the ellipse defined by x2 + 4 y2 ≤ 1.. (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 ...Post your question

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