Quiz STAT351 5/11/2021
加拿大统计代考 Suppose that X1,X2,X3,X4 are independent U(0, 1)-distributed random variables and let (X(1),X(2),X(3),X(4)) be the corresponding order statistic.
- 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 [8]
Defining all terms that you use, show that:
Q2 [10] 加拿大统计代考
Suppose that , … , are iid exp(1) RV:
Determine:
a)distributionand density of X(1)
b)distribution and density of X(n)
c)Joint distribution and density of X (1) and X(n)
d)Distribution of theRange
Q3 [10] 加拿大统计代考
Suppose that X1,X2,X3,X4 are independent U(0, 1)-distributed random variables and let (X(1),X(2),X(3),X(4)) be the corresponding order statistic. Compute:
a) ( X(2)+ X(3) ≤ 5)
b) ( X(2)≤ X4 (1))
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