Study Guides (238,380)
Statistics (153)
STAT 330 (19)
Midterm

# Midterm2_review.pdf

1 Page
160 Views

School
University of Waterloo
Department
Statistics
Course
STAT 330
Professor
Christine Dupont
Semester
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

OR

Don't have an account?

Join OneClass

Access over 10 million pages of study
documents for 1.3 million courses.

Join to view

OR

By registering, I agree to the Terms and Privacy Policies
Just a few more details

So we can recommend you notes for your school.