STAT 351
Midterm 1 October, 2021
美国统计代考 Please show all your work. It is YOUR responsibility to convince me that you know what you are doing. Clarity, completeness, and organization count.
- 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 count.
Q1 [20 marks] 美国统计代考
Let X and Y be identically and independently distributed standard normal random variables:
a)Findthe joint density function of U = X + Y and V =
b)Are U and Vindependent?
c)What is the marginal distribution ofU?
d)What is the marginal distribution of V?
Q2 [20 marks]
Suppose that random variables X and Y have joint p.d.f.
Determine the marginal density function of U and V.
Q3 [10 marks] 美国统计代考
Prove that: 
