DEPARTMENT OF MATHEMATICS & STATISTICS
STAT 351
Midterm November, 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:?|Λ = ? ~ ????(?)
- 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.
- 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
Q1 [20 marks] Statistics统计学代考
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)
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:
?|Λ = ? ~ ????(?) ???ℎ Λ~Γ(?, ?)
Where:
And
Find:
a) Marginal distribution of X
b) f(λ|x)
c) Name the distribution in b)