Let T have an exponential distribution with parameter λ. Let Y = √T . a) Find the density of Y b) Find the expectation of Y, correct to two decimal places, for λ = 3. c) A random number generator produces uniform [0, 1] random numbers. How could you use these to generate random numbers which have the distribution of Y ?

Let T have an exponential distribution with parameter λ. Let Y = √T . a) Find the density of Y b) Find the expectation of Y, correct to two decimal places, for λ = 3. c) A random number generator produces uniform [0, 1] random numbers. How could you use these to generate random numbers which have the distribution of Y ?

A First Course in Probability (10th Edition)

10th Edition

ISBN:9780134753119

Author:Sheldon Ross

Publisher:Sheldon Ross

Chapter1: Combinatorial Analysis

Section: Chapter Questions

Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...

See similar textbooks

Similar questions

Find the moment-generating function of the contin-uous random variable X whose probability density is given by f(x) =1 for 0 < x < 10 elsewhere and use it to find μ1,μ2, and σ2.
Find the moment generating function MU(t) for the standard uniform random variable U (the continuous random variable whose density function is 1 on [0,1] and 0 elsewhere)
A point D is chosen on the line AB, whose midpointis C and whose length is a. If X, the distance from D toA, is a random variable having the uniform density withα = 0 and β = a, what is the probability that AD, BD,and AC will form a triangle?
Suppose that the random variables X and Y have a joint density function given by: f(x,y) = {c(2x+y) for 2≤x≤6 and 0≤y≤5, 0 otherwise P(3 < X < 5, Y >1), P(X < 3), P(X +Y > 5), Find the joint distribution function (cdf),
Suppose that X, Y , and Z are random variables with a joint density f(x, y, z) = ( 6/((1+x+y+z)^4)) , when x, y, z > 0, and 0, otherwise. Determine the distribution of X + Y + Z.
Find the moment generating function for the random variable X whose density function is f(x). fx = 2x 0<x<1 MX(t) = _______________________________________
Given the random variables X and Y having the following joint density: f(x, y) = 2(x + y) for 0 < y < x < 1. A) Compute the conditional pdfs: fX│Y (x) and fY│X (y). B) Are X and Y independent?
Suppose that the random variables X and Y have a joint density function f(x,y).prove that Cov(X,Y)=0 if E(X|Y=y) does not depend on y
Let X denote the reaction time, in seconds, to a certain stimulus and Y denote the temperature (◦F) at which a certain reaction starts to take place. Suppose that two random variables X and Y have the joint density
Let X and Y be a pair of continuous random variables with a joint density fx,y(x,y). Assume that fx,y(x,y) = cxy for x greater than or equal to 0, y greater than or equal to 0, and x + y less than or equal to 1. Here c is a constant. Assume that fx,y(x,y) is 0 elsewhere. What is the constant c equal to? With the value of c, what is E[XY]?
Suppose that the random variables X, Y, Z have multivariate PDFfXYZ(x, y, z) = (x + y)e−z for 0 < x < 1, 0 < y < 1, and z > 0. Find (a) fXY(x, y), (b) fYZ(y, z), (c) fZ(z)
Suppose that the random variables X and Y have a joint density function given by: f(x,y)={cxy for 0≤x≤2 and 0≤y≤x, 0 otherwise Find the constant c, P(Y≥1/2), P(X < 2, Y >1/2), P(X < 1), Determine whether X and Y are independent.