Problem 1. (5 marks. 3. 2) Assume X ~ Gamma(01, β) and Y ~ Gamma(O2, β)...
LetX-Gamma(α = 2, β = 4), Y-Gamma(α = 3, β = 4), X & Y are independent, Z,- , Z,-X + Y. X+Y a) (3 pts) State the joint pdf ofX and Y. Simplify the expression, clearing all Г's. b) (9 pts) Find the joint pdf of Zi and Z2, using the two variable transformation method. In addition, clearly write the support for this joint pdf. When done, your answer should include the expression c) (5 pts) You should see...
2. LetX~Gamma(α = 2, β = 4), Y~Gamma(α = 3, β = 4), X & Y are independent, Z,-x+r, Z,-X + Y a) (3 pts) State the joint pdf oEX and Y. Simplify the expression, clearing all b) (9pts) Find the joint pdf of Z and Z, using the two variable transformation method. In addition, clearly write the support for this joint pdf. When done, your answer should include the expression Z1Z21,2)2048 2048 11 )24e-22/4 c) (5 pts) You should...
2. LetX-Gamma(α = 2, β = 4), Y-Gam ma (α = 3, β = 4), X & Y are independent, Z1 = , Z,-X + Y a) (3 pts) State the joint pdf ofX and Y. Simplify the expression, clearing all Г's. b) (9 pts) Find the joint pdf of Zi and Zz, using the two variable transformation method. In addition, clearly write the support for this joint pdf. When done, your answer should include the expression (5 pts) You...
Answer each of the following questions. You have to show all your work to get full e Problema 1. (5 marks; 3, 2) Assume X ~ Gamma(ai, β) and Y ~ Gamma(a2, β) are independent random variables. a) Compute the joint density of U = X X+Y and VX/X+Y), be sure to include the support/domain.
Problem 5) Let X and Y be independent gamma RVs with parameter (a, 1) and (3, 1), respec- tively. a) Show that X + Y is also gamma RV with parameters (a +3,1). b) Compute the joint density of U = X + Y and V = ty
Problem 8: Suppose the Ý, , , Y, β are independent and identically distributed random variables in the interval (0,1) with individual densities where β 〉 0. Further suppose that β has marginal density f(β) 482 exp(-2β). Derive f(B|Y, Y). Identify the distributional family for B and describe its parameters.
Problem 8: Suppose the Ý, , , Y, β are independent and identically distributed random variables in the interval (0,1) with individual densities where β 〉 0. Further suppose that...
5. (a) (6 marks) Let X be a random variable following N(2.4). Let Y be a random variable following N(1.8). Assume X and Y are independent. Let W-min(x.Y). Find P(W 3) (b) (8 marks) The continuous random variables X and Y have the following joint probability density function: 4x 0, otherwise Find the joint probability density function of U and V where U-X+Y and -ky Also draw the support of the joint probability density function of Uand V (o (5...
Suppose X and Y are independent and
Prove the following
a) U=X+Y~gamma(α + β,γ)
b) V=X/(X + Y ) ∼ beta(α,β)
c) U, V independent
d) ~gamma(1/2,
1/2) when W~N(0,1)
X ~ gammala, y) and Y ~ gamma(6, 7) We were unable to transcribe this image
1. Consider two random variables X and Y with joint density function f(x, y)-(12xy(1-y) 0<x<1,0<p<1 otherwise 0 Find the probability density function for UXY2. (Choose a suitable dummy transformation V) 2. Suppose X and Y are two continuous random variables with joint density 0<x<I, 0 < y < 1 otherwise (a) Find the joint density of U X2 and V XY. Be sure to determine and sketch the support of (U.V). (b) Find the marginal density of U. (c) Find...
1. Suppose that Y ∼ Gamma(α, β) and c > 0 is a constant. (a)
Derive the density function of U = cY. (b) Identify the
distribution of U as a standard distribution. Be sure to identify
any parameter values. (c) Can you find the distribution of U using
MGF method also?
I. Suppose that Y ~ Gamma(α, β) and c > 0 is a constant. (a) Derive the density function of U cY. (b) Identify the distribution of U...