Let X~UNIF(0,1), and Y=-lnX. Then what is the density function of Y where nonzero?
Let X~UNIF(0,1), and Y=-lnX. Then what is the density function of Y where nonzero?
Suppose that U~Unif[0,1]. Let . Find the probability density function of Y.
9 Let X and Y have the joint probability density function f(x, y) ={4x for 。< otherwise a) What is the marginal density function of Y, where nonzero? b)Are X and Y stochastically independent 9 Let X and Y have the joint probability density function f(x, y) ={4x for 。
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() =
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.
Let X ~ Unif(0,1). Find a function of X that has CDF F(x) = 1 ̶ x ̶ p for p > 0 (this is the Pareto distribution).
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
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.
(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 =
If X and Y have a joint density given by f(x, y) = 2, for 0 < y < x < 1 0, elsewhere (a) If V = −lnX, what is the density of V ? (b) If V = −lnX and W = X + Y , what is the joint density of V and W? Sketch the region for which the joint density is nonzero.
Please show both joint density function of (X,Y) and the name of the distribution. Exercise 6.17. Let U and V be independent, U Unif(0,1) and V~ Gamma(2, x) which means that V has density function 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 the more general Exercise 6.50. fv (v-λ-e-Av for