Statistics统计学代考-STAT 351-Midterm代写

Statistics统计学代考

DEPARTMENT OF MATHEMATICS & STATISTICS

Statistics统计学代考 LetX1，X，X3 be independent Exp(1) random variables. Compute P(X(1)＝X1,X(2)＝X2,X(3)＝X3)You are given that:?|Λ = ? ~ ????(?)

I affirm that I will not give or receive any unauthorized help on this exam, and that all work will be my own. This is not an open book quiz.

Nobooks or lectures notes allowed for this exam.
Please show all your work. It is YOUR responsibility to convince me that you know what you are doing. Clarity, completeness, and organization

Given the joint density function fx,y^（^x,y^）＝

a)Determinethe marginal density functions f(x) and fY(y)

b)Explainwhether or not X and Y are independent

c)Findthe conditional density fY_|X(y)

d) Find E(X|Y)

LetX₁，X，X₃ be independent Exp(1) random variables. Compute P(X₍₁₎＝X₁,X₍₂₎＝X₂,X₍₃₎＝X₃)

You are given that:

?|Λ = ? ~ ????(?) ???ℎ Λ~Γ(?, ?)

Where:

And

Find:

a) Marginal distribution of X

b) f(λ|x)

c) Name the distribution in b)