Study Guides
(238,380)

Canada
(115,122)

University of Waterloo
(5,557)

Statistics
(153)

STAT 330
(19)

Christine Dupont
(13)

Midterm

# Midterm2_review.pdf

Unlock Document

University of Waterloo

Statistics

STAT 330

Christine Dupont

Fall

Description

Midterm 2 Review
1. Suppose X ▯ UNIF(0;1) and Y ▯ UNIF(0;1) independently. Find the joint p.d.f. of
1=2
U = (▯2logX) cos(2▯Y )
1=2
V = (▯2logX) sin(2▯Y ):
2. Let X ▯ N(0;1) and Y ▯ N(0;1) independently. Let W = X and Z = Y.
X
(a) Find the joint p.d.f. of W and Z.
(b) Find the marginal d.f. of Z.
iid n +
3. Let X1;:::;X n ▯ Unif(0;1). Deﬁne Y n ▯ i=1X i where n 2 Z .
(a) Derive the m.g.f. of (▯log(X );▯log(X );:::;▯log(X )).
1 2 n
(b) Hence, what is the distribution of ▯lognY ).
1
(c) Show that ▯ nlog(Yn) converges in probability to 1 as n tends to inﬁnity.
1
4.

More
Less
Related notes for STAT 330