Question 2 (5101) Suppose that X and Y are independent, and that Z = X+Y. If...

Question

Question

Question 2 (5101) Suppose that X and Y are independent, and that Z = X+Y. If X ~ Exp(B = 1) and Y~ Unif(-1,1], what is the de

Answer 1

Answer #1

- Вх ,X> Let Xn exp (B=1) then pdf of Xis, f(x) = Be x 7.0 and YN Unif (-1,] theo pdf of Y is, f cy) = e 1 a sagsb b-a 1 -ey

marginal density of z is, g (z) = f g (z, v) dv - Z ✓ = e e dr po 2 = erz er dr 2 -1 - Z V H 11 es - 2 = - Z e نم 2 - e-Z [ 2

Answer 2

Similar Homework Help Questions

Question 2 (5101) Suppose that X and Y are independent, and that Z = X+Y. If...

Question 2 (5101) Suppose that X and Y are independent, and that Z = X+Y. If X Exp(B = 1) and Y~ Unif(-1,1], what is the density of Z?
Problem 5 Suppose X and Y are independent random variables following Uniform[0, 1]. Let Z- (X +Y)/2. (1) Calculate the cumulative density of z. (2) Calculate the density of Z. Problem 5 Suppose...

Problem 5 Suppose X and Y are independent random variables following Uniform[0, 1]. Let Z- (X +Y)/2. (1) Calculate the cumulative density of z. (2) Calculate the density of Z. Problem 5 Suppose X and Y are independent random variables following Uniform[0, 1]. Let Z- (X +Y)/2. (1) Calculate the cumulative density of z. (2) Calculate the density of Z.
7. (EXTRA CREDIT) Suppose the X ~ Exp(1) and Y ~ Exp(1) are independent. Let Z...

7. (EXTRA CREDIT) Suppose the X ~ Exp(1) and Y ~ Exp(1) are independent. Let Z = X/Y. How is Z distributed? Include all the details in your derivation.

Question 3 (4101) Suppose that X, Y and Z are all independent of each other, with...

Question 3 (4101) Suppose that X, Y and Z are all independent of each other, with the following distributions: X Poisson (1) Y Gamma(,b) Z~ N(0,1) Define A as the sum: A = X+Y+Z a What is E[A]? b What is the MGF of A? (you don't need to re-derive the individual mgfs) c Use ma(t) to find E[A] (should match part a)
1. Suppose that E(X) E(Y) E(Z) 2 Y and Z are independent, Cov(X, Y) V(X) V(Z)...

1. Suppose that E(X) E(Y) E(Z) 2 Y and Z are independent, Cov(X, Y) V(X) V(Z) 4, V(Y) = 3 Let U X 3Y +Z and W = 2X + Y + Z 1, and Cov(X, Z) = -1 Compute E(U) and V (U) b. Compute Cov(U, W). а.
Let X have the pdf defined for 0<x<2. Let Y~Unif(0,1). Suppose X and Y are independent....

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() =

4 Suppose that W, X, Y, Z are independent random variables, each with probability density function...

4 Suppose that W, X, Y, Z are independent random variables, each with probability density function f(t) -4t3,0st s 1. Find. (b) fw.x.y.z(w, x, y, z) (c) Fxy (x,y)
2. Suppose X and Y are independent random variables with the pdf (probability density func- tion)...

2. Suppose X and Y are independent random variables with the pdf (probability density func- tion) f(x) e-2 for x > 0. (a) What is the joint probability density function of (X, Y)? (b) Define W-X-Y, Z = Y, then what is the Joint probability density function fw.z(w, z) for (W, Z). (c) Determine the region for (w, z) where fw.z is positive. (d) Calculate the marginal probability density function for W.
2. Suppose X and Y are independent random variables with the pdf (probability density func- tion)...

2. Suppose X and Y are independent random variables with the pdf (probability density func- tion) f(x)- for x > 0. (a) What is the joint probability density function of (X, Y)? (b) Define W = X-Y, Z = Y, then what is the joint probability density function fw,z(w, z) for (W, Z). (c) Determine the region for (w, z) where fw,z is positive. (d) Calculate the marginal probability density function for W

1. Suppose that the joint density of X and Y is given by exp(-y) (1- exp(-x)), if 0 S y,0 syS oo ...

1. Suppose that the joint density of X and Y is given by exp(-y) (1- exp(-x)), if 0 S y,0 syS oo exp(-x) (1- exp(-y)), if 0SyS ,0 oo (e,y)exp(-y) Then . The marginal density of X (and also that of Y), ·The conditional density of Y given X = x and vice versa, Cov(X, Y) . Are X and Y independent? Explain with proper justification. 1. Suppose that the joint density of X and Y is given by exp(-y)...