Suppose that U~Unif[0,1]. Let . Find the probability density function of Y.
Suppose that U~Unif[0,1]. Let . Find the probability density function of Y.
Let X~UNIF(0,1), and Y=-lnX. Then what is the density function of Y where nonzero?
Suppose that U Unif(-2,5) and that Y = g(u) = u? a Find the density of Y, fy(y) b Find E[Y] using this derived density c Find E[U?] using the density of U (should match part b) Hint: draw the problem
Exercise 6.17. Let U and V be independent, U~ Unif(0,1), and V~ Gamma(2.A) which means that V has density function fv(1) λ2e-W for v0 and zero elsewhere. Find the joint density function of (X, Y)-. (UV, ( 1-U)V). Identify the joint distribution of (X, Y) In terms of named distributions. This exercise and Example 6.44 are special cases of
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() =
(1 point) 5.8 Assume that X ~ Unif[-1, 5] and let fy(y) be the probability density function of the random variable Y = X. Find fy(4). Give your answer as a fraction. Answer =
Problem 4. Let X~N(0,1) and Ye. Find the probability density function of Y. This random variable Y is called a log-normal random variable and is frequently used in mathematical modeling of asset prices.
Let X ~ U[0,1] be a standard uniform random variable. Find the probability density functions (pdf's) of the following random variables: iii) Y = 1/x0.5
1. For X ~U(0,1), define Y = XP, PE 0. What is the probability density function of Y? Hint: answer may depend on the sign of p.
5. Let X be uniformly distributed over (0,1). a) Find the density function of Y = ex. b) Let W = 9(X). Can you find a function g for which W is an exponential random variable? Explain.
a) Let X-Unif(0,1). Derive the pdf of Y =-ln(1-X) Remember to provide its support. Let X-N(1,02). Derive the pdf of Y-ex and remember to provide its support. b) Hint for both parts: First work out the cdf of Y, and then use it to find the density of Y.