Let X,Y ~ Uniform (0,1) be independent. Find the PDF for X-Y and X/Y.
Let X,Y ~ Uniform (0,1) be independent. Find the PDF for X-Y and X/Y.
Let X and Y be iid uniform random variables on [0,1]. Find the pdf of Z=X+Y
Problem 3 Let X be Uniform(0,1) and Y be Exponential (1). Assume that X and Y are independent. i. Find the PDF of Z- X +Y using convolution. ii. Find the moment generating function, øz(s), of Z. Assume that s< 0. iii. Check that the moment generating function of Z is the product of the moment gen erating functions of X and Y Problem 3 Let X be Uniform(0,1) and Y be Exponential (1). Assume that X and Y are...
Let X have the pdf defined for 0<x<2. Let Y~Unif(0,1). Suppose X and Y are independent. Find the distribution of X-Y. fx() =
. Let Y and Z be independent uniform random variables on the interval [0,1]. Let X = ZY. (a) Compute E(XY). (b) Compute E(X).
Let X and Y be continuous and independent random variables, both with uniform distribution (0,1). Find the functions of probability densities of (a) X + Y (b) X-Y (c) | X-Y |
Let X, Y, Z be independent uniform random variables on [0,1]. What is the probability that Y lies between X and Z.
4. Let Y and Z be independent uniform random variables on the interval [0,1]. Let X Z (a) Compute E(XTY). (b) Compute E(X).
# 11 11. If X U(0.1) and Y (0,1) independent random variables, find the joint pdf of (X + Y, X-Y) Also compute marginal pdf of X+Y. If XExponentialia
The numbers x, y, z are independent with uniform distribution on [0,1]. Find the probability that one can construct a triangle with sides length x, y, z.
Let the random variable X have a uniform distribution on [0,1] and the random variable Y (independent of X) have a uniform distribution on [0,2]. Find P[XY<1].