1. Develop a random variate (composition method) generator for the random variable X with the probability density function where I represents the indicator function. 5 e*I(x<0)+=e³I(x>0) 6

Q: Let V = X+ Y and W = X/Y. Show that the joint density of V and W is given by 1 fv,w(v, w) = 27 /w(w…

A:

Q: Suppose X is a continuous random variable whose probability density function is f(x) =  xe−x x ≥ 0…

A: The Probability Density Function(PDF) defines the probability function representing the density of a…

Q: A random variable x has a probability density π πχ 1 = {i ces + 8 0 Find the following a) mean value…

A: Please find the explanation below. Thank you.

Q: 3. x and y are independent zero mean Gaussian random variables with variance of and o. Let z = (x +…

A: Here we have x and y, two independent zero mean Gaussian random variables with σ2x and σ2y.  So the…

Q: generating functions: a m(t) = [(1/3)e' +(2/3)]5. e' h m(t).

A: Note: According to the Bartleby guidelines expert solve only one question and rest can be reposted.

Q: 2. The following density function describes the random variable X. 1 2x+1-20 if 0 _=1 < x < 0+₁ 2 2…

A: