Carnegie Mellon University Department of Statistics
36-705 Intermediate Statistics Homework #2
Solutions
September 15, 2016
Problem 1 [25 pts.]
Let X have mean 0. We say that X is sub-Gaussian if there exists > 0 such that
log (E[etX ])
t2 2
2
for all t.
Carnegie Mellon University Department of Statistics
36-705 Intermediate Statistics Homework #1
Solutions
September 1, 2016
Problem 1: Wasserman 1.3
Let be a sample space and let A1 , A2 , . . . be events. Define Bn =
i=n Ai and Cn = i=n Ai .
(a) Show tha
Carnegie Mellon University Department of Statistics
36-705 Intermediate Statistics Homework #4
Solutions
October 6, 2016
Problem 1 [30 pts.]
(a) [20 pts.] Find a minimal sufficient statistic.
p(y n ; , )
A statistic T is minimal sufficient if
does not dep
Carnegie Mellon University Department of Statistics
36-705 Intermediate Statistics Homework #3
Solutions
September 29, 2016
Problem 1 [15 pts.]
Let C = A B. Show that
sn (C) sn (A) + sn (B)
where sn denotes the shattering number.
Solution.
Let F be a fini
Practice Test for Test II
1. Let X1 , . . . , Xn Uniform(, ) where > 0.
(a) Find the maximum likelihood estimator bn .
(b) Find a minimal sufficient statistic.
P
(c) Show that bn .
(d) Find the limiting distribution of n( bn ).
2. Let X Bernoulli() be a s