(11 pts) Use the Distribution Function Method on this problem: The random variable Y has an...
5. (11 pts) Use the Distribution Function Method on this problem: The random variable Y has an exponential distribution with parameter β. Let ?? = √??. Find the pdf of U. Note: U has a Weibull distribution. You will see the Weibull distribution many times in this course 5. (11 pts) Use the Distribution Function Method on this problem: The random variable Y has an exponential distribution with parameter B. Let U-VY. Find the pdf of U. Note: Uhas a...
6. (11 pts) Use the Distribution Function Method here: The random variable ??~????????(∝= 4, ?? = 2). Let ?? = ??4. Find the pdf of U. (1 l pts) Use the Distribution Function Method here: The random variable Y~Beta(α= 4, β = 2). Let U 6. Y4, Find the pdf of U.
(11 pts) Use the Distribution Function Method here: The random variable y-Beta( Let U Y4. Find the pdf of U. 4,β-2). 6.
6. (11 pts) Use the Distribution Function Method here: The random variable Y~ Beta(o4,B 2). Let U-Y4. Find the pdf of U.
Problem The random variable X is exponential with parameter 1. Given the value r of X, the random variable Y is exponential with parameter equal to r (and mean 1/r) Note: Some useful integrals, for λ > 0: ar (a) Find the joint PDF of X and Y (b) Find the marginal PDF of Y (c) Find the conditional PDF of X, given that Y 2. (d) Find the conditional expectation of X, given that Y 2 (e) Find the...
Problem 5. Let X be a continuous random variable with a 2-paameter exponential distribution with parameters α = 0.4 and xo = 0.45, ie, ;x 2 0.45 x 〈 0.45 f(x) = (2.5e-2.5 (-0.45) Variable Y is a function of X: a) Find the first order approximation for the expected value and variance of Y b) Find the probability density function (PDF) of Y. c) Find the expected value and variance of Y from its PDF Problem 5. Let X...
4. (9 pts) Suppose the random variable Y has a geometric distribution with parameter p. Let ?? = √?? 3 3 . Find the probability distribution of V 3 4. (9 pts) Suppose the random variable Y has a geometric distribution with parameter p. Let V 3 Find the probability distribution of.
Let Y be a random variable with probability density function, pdf, f(y) = 2e-2y, y > 0. Determine f (U), the pdf of U = VY.
Problem 3 [5 points) (a) [2 points] Let X be an exponential random variable with parameter 1 =1. find the conditional probability P{X>3|X>1). (b) [3 points] Given unit Gaussian CDF (x). For Gaussian random variable Y - N(u,02), write down its Probability Density Function (PDF) [1 point], and express P{Y>u+30} in terms of (x) [2 points)
Use the method of distribution functions 2. (5 marks) Consider a random variable Y with density function 3y2 0 ,else Find the probability density function of U 4-Y