UC Berkeley Department of Statistics STAT 210A: Introduction to Mathematical Statistics Problem Set 5- Solutions Fall 2007 Issued: Thursday, September 27 Due: Thursday, October 4 Problem 5.1 (a) For the Gamma density, we have: p(x|) exp log(x) px + log p
UC Berkeley Department of Statistics STAT 210A: Introduction to Mathematical Statistics Problem Set 10- Solutions Fall 2007 Issued: Thursday, December 8 Due: Thursday, December 15 Problem 10.1 a) The action space is given by A = cfw_0, 1. For = 0 , the lo
UC Berkeley Department of Statistics STAT 210A: Introduction to Mathematical Statistics Problem Set 8 Fall 2006 Issued: Thursday, October 26, 2006 Due: Thursday, November 2, 2006
Some useful notation: The pth quantile of a continuous random variable with
UC Berkeley Department of Statistics STAT 210A: Introduction to Mathematical Statistics Problem Set 1 Fall 2007 Issued: Thursday, August 30
d p m.s.
Due: Thursday, September 6
Notation: The symbols cfw_, , denote convergence in distribution, probability
UC Berkeley Department of Statistics
STAT 210A: Introduction to Mathematical Statistics Problem Set 5 - Solutions Fall 2008 Issued: Tuesday, September 29, 2009 Problem 5.1 First, notice that we can rewrite: p(x; ) = exp [x log log ( log(1 )] so p belongs
UC Berkeley Department of Statistics STAT 210A: Introduction to Mathematical Statistics Problem Set 1- Solutions Fall 2006 Issued: Thursday, August 31, 2006 Problem 1.1 Solution to 1. Let: Yn = 0, n, with probability 1
1 with probability n 1 n
Due: Thurs
UC Berkeley Department of Statistics STAT 210A: Introduction to Mathematical Statistics Problem Set 7 Fall 2006 Issued: Thursday, October 19, 2006 Due: Thursday, October 26, 2006
Problem 7.1 p d d Show that if Xn X > 0 and Xn /Yn 1, then Yn X. Problem 7.2
UC Berkeley Department of Statistics STAT 210A: Introduction to Mathematical Statistics Problem Set 6 Fall 2006 Issued: Thursday, October 5, 2006 Problem 6.1 a) Using the Rao-Blackwell theorem and considering the quadratic error loss function L(, ) = ( -
UC Berkeley Department of Statistics STAT 210A: Introduction to Mathematical Statistics Problem Set 6 Fall 2006 Issued: Thursday, October 5, 2006 Due: Thursday, October 12, 2006
Problem 6.1 In the inverse binomial sampling procedure, N is a random variabl
UC Berkeley Department of Statistics STAT 210A: Introduction to Mathematical Statistics Problem Set 5 Fall 2006 Issued: Thursday, September 14, 2006 Due: Thursday, September 21, 2006
Graded exercises
Problem 5.1 a) We want to show that R(, ) = E ( (X-) )
UC Berkeley Department of Statistics STAT 210A: Introduction to Mathematical Statistics Problem Set 5 Fall 2006 Issued: Thursday, September 28, 2006 Due: Thursday, October 5, 2006
A useful definition for this problem set: Definition: An equalizer procedur
UC Berkeley Department of Statistics STAT 210A: Introduction to Mathematical Statistics Problem Set 4 Fall 2006 Issued: Thursday, September 21, 2006 Due: Thursday, September 28, 2006
Graded exercises
Problem 4.1 First, notice that we can rewrite: p(x; ) =
UC Berkeley Department of Statistics STAT 210A: Introduction to Mathematical Statistics Problem Set 3 Fall 2006 Issued: Thursday, September 14, 2006 Due: Thursday, September 21, 2006
Graded exercises
Problem 3.1 (a) To prove that, we massage the density e
UC Berkeley Department of Statistics STAT 210A: Introduction to Mathematical Statistics Problem Set 2 Fall 2006 Issued: Thursday, September 7, 2006 Due: Thursday, September 14, 2006
Graded exercises
Problem 2.1 From the distribution of X, we have:
n
P (X
UC Berkeley Department of Statistics STAT 210A: Introduction to Mathematical Statistics Problem Set 9- Solutions Fall 2007 Issued: Thursday, December 1 Due: Thursday, December 8 Problem 9.1 We want to prove that, for all , P ( S (X ) 1 . To prove that, we
UC Berkeley Department of Statistics STAT 210A: Introduction to Mathematical Statistics Solutions - Problem Set 7 Fall 2006 Issued: Thursday, September 14, 2006 Due: Thursday, September 21, 2006
Graded exercises
Problem 7.1 p Y Let Zn = Xn , we have that
UC Berkeley Department of Statistics STAT 210A: Introduction to Mathematical Statistics Solutions - Problem Set 8 Fall 2006 Issued: Thursday, November 2, 2006 Due: Thursday, November 9, 2006
Graded exercises
Problem 8.1 (a) From the definitions given, we
UC Berkeley Department of Statistics STAT 210A: Introduction to Mathematical Statistics Problem Set 4 Fall 2006 Issued: Thursday, September 21, 2006 Note: For this problem set, "Norway". Problem 4.1 By Taylor series expansion, we have the identity - log(1
UC Berkeley Department of Statistics STAT 210A: Introduction to Mathematical Statistics Problem Set 3 Fall 2006 Issued: Thursday, September 14, 2006 Due: Thursday, September 21, 2006
Graded
Problem 3.1 The inverse Gaussian distribution IG(, ) has density
UC Berkeley Department of Statistics STAT 210A: Introduction to Mathematical Statistics Problem Set 2 Fall 2006 Issued: Thursday, September 7, 2006 Due: Thursday, September 14, 2006
Graded problems
Problem 2.1 Suppose that Xi , i = 1, . . . , n are i.i.d.
UC Berkeley Department of Statistics STAT 210A: Introduction to Mathematical Statistics Problem Set 1 Fall 2006 Issued: Thursday, August 31, 2006 Due: Thursday, September 7, 2006
Problem 1.1 p Given a sequence of random variables such that Yn , give one e
UC Berkeley Department of Statistics STAT 210A: Introduction to Mathematical Statistics Midterm Examination-Solutions Fall 2006 Problem 1.1 [18 points total] Suppose that Xi , i = 1, . . . , n are i.i.d. samples from the uniform Uni[0, ] distribution. (a)
UC Berkeley Department of Statistics STAT 210A: Introduction to Mathematical Statistics Solutions - Problem Set 11 Fall 2006 Issued: Thursday, November 9, 2006 Due: Thursday, November 16, 2006
Graded exercises
Problem 11.1 a) The functional h(F ) = F (a)
UC Berkeley Department of Statistics STAT 210A: Introduction to Mathematical Statistics Problem Set 11 Fall 2006 Issued: Thursday, November 30, 2006 Due: Thursday, December 7, 2006
Problem 11.1 Recall that a statistical function h is said to be continuous
UC Berkeley Department of Statistics STAT 210A: Introduction to Mathematical Statistics Solutions - Problem Set 10 Fall 2006 Issued: Thursday, November 9, 2006 Due: Thursday, November 16, 2006
Graded exercises
Problem 10.1 a) For each i, Zi = I(Yi > 0 ) f
UC Berkeley Department of Statistics STAT 210A: Introduction to Mathematical Statistics Problem Set 10 Fall 2006 Issued: Thursday, November 9, 2006 Due: Thursday, November 16, 2006
Problem 10.1 (A non-parametric hypothesis test) A set of i.i.d. samples Y1
UC Berkeley Department of Statistics STAT 210A: Introduction to Mathematical Statistics Solutions - Problem Set 9 Fall 2006 Issued: Thursday, November 2, 2006 Due: Thursday, November 9, 2006
Graded exercises
Problem 9.1 (a) First, notice that ga () = P(X1
UC Berkeley Department of Statistics STAT 210A: Introduction to Mathematical Statistics Problem Set 9 Fall 2006 Issued: Thursday, November 2, 2006 Due: Thursday, November 9, 2006
Some useful notation: Let denote the CDF of a standard normal variate, and l
UC Berkeley Department of Statistics STAT 210A: Introduction to Mathematical Statistics Problem Set 8- Solutions Fall 2007 Issued: Thursday, October 25 Due: Thursday, December 1 Problem 8.1 (a) For a Bernoulli random variable, we have: E X = var X = (1 )
UC Berkeley Department of Statistics STAT 210A: Introduction to Mathematical Statistics Problem Set 7- Solutions Fall 2007 Issued: Thursday, October 18 Due: Thursday, October 25 Problem 7.1 (a)
E(|Xi |) = 2 =
0
x
x2 1 e 22 dx = 2
0
t e 2 dt 2
t=
x2 2
2 C