# Question

Let X be a Gaussian random variable with zero mean and arbitrary variance, σ2. Given the transformation Y= X3, find fY (y).

## Answer to relevant Questions

In each of the following cases, find the value of the parameter a which causes the indicated random variable to have a mean value of 10. (a) (b) (c) Suppose a random variable has some PDF given by fX(x). Find a function g(x) such that Y= g(X) is a uniform random variable over the interval (0, 1). Next, suppose that X is a uniform random variable. Find a function g(x) ...For a constant k, two discrete random variables have a joint PMF given by (a) Find the value of the constant c in terms of k. (b) Find the marginal PMFs, PM (m) and PN (n). (c) Find Pr (M + N < k/2). 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 ...Suppose two random variables and are both zero mean and unit variance. Furthermore, assume they have a correlation coefficient of ρ. Two new random variables are formed according to: W = aX + bY, Z = cX + dY, Determine ...Post your question

0