Statistics统计学代考

## MidtermNovember,2021

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:𝑋|Λ = 𝜆 ~ 𝑃𝑜𝑖𝑠(𝜆)

1. Please copy and sign the following honour codestatement:

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.

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

### Q1 [20 marks]    Statistics统计学代考

Given the joint density function fx,yx,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)

### Q2 [10 marks]  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)

### Q3 [10 marks]  Statistics统计学代考

You are given that:

𝑋|Λ = 𝜆 ~ 𝑃𝑜𝑖𝑠(𝜆) 𝑤𝑖𝑡ℎ Λ~Γ(𝛼, 𝜃)

Where:

And

Find:

a) Marginal distribution of X

b) f(λ|x)

c) Name the distribution in b)