APPM/MATH 4/5520
Problem Set Four (Due Wednesday, September 23rd)
1. Suppose that X1 , X2 , . . . , Xn is a random sample from a distribution with pdf f and cdf F .
Show that
n
ln F (Xi ) 2 (2n).
2
i=1
2. Let X1 , X2 , . . . , Xn be a random sample from t

APPM/MATH 4/5520
Problem Set Eight (Due Wednesday, October 28th)
iid
1. Let X1 , X2 , . . . , Xn N (, 2 ). Find a 100(1 )% condence interval for 2 based on the
sample variance and a 2 critical value(s).
2. Let X1 , X2 , . . . , Xn be a random sample from

APPM/MATH 4/5520
Problem Set Seven (Due Wednesday, October 14th)
1. Suppose that a random sample of size 12, taken from a N (, 3) distribution, results in a
sample mean of 5.7. Give an 88% condence interval for the true mean .
2. Suppose that a random sam

APPM/MATH 4/5520
Problem Set Five (Due Wednesday, October 14th)
1. Recall our denition of a t-distribution: Let Z N (0, 1) and W 2 (n) be independent
random variables. Since the dsitribution of W depends on n, I will write W as Wn . Dene
T = Tn =
Z
.
Wn /

APPM/MATH 4/5520, Fall 2015
Problem Set Two (Due Wednesday, September 9th)
1. Compute the mean of the (, ) distribution by integrating without integrating.
2. Suppose that X is uniformly distributed on the interval (0, 1). (We write X unif (0, 1).)
(a) De

APPM/MATH 4/5520, Fall 2015
Problem Set One (Due Wednesday, September 2nd)
Welcome to Problem Set One! This is the only assignment where you will encounter some problems
and topics that we have not covered in class. The point is to force you to catch up w

APPM/MATH 4/5520
Problem Set Nine (Due Wednesday, November 4th)
1. Let X1 , X2 , . . . , Xn be a random sample from the (, ) distribution. Suppose that is
xed and known.
(a) Find the MME of .
(b) Find the MLE of .
(c) Which estimator (MME or MLE) has smal

APPM/MATH 4/5520, Fall 2015
Problem Set Three (Due Wednesday, September 16th)
1. Derive the moment generating function for the exponential distribution with rate . Be sure
to include an explanation as to why we need t < .
2. Let X geom0 (p).
(a) Compute t

APPM/MATH 4/5520
Problem Set Five (Due Wednesday, September 30th)
1. Suppose that X1 , X2 , . . . , Xn is a random sample from the (, ) distribution where is
xed and known. Find an unbiased estimator of .
2. Let X1 , X2 , . . . , Xn be a random sample fro

APPM/MATH 4/5520
Problem Set Ten (Due Wednesday, November 11th)
1. Let X1 , X2 , . . . , Xn be a random sample from the P oisson() distribution.
(a) Find the Cramr-Rao lower bound (CRLB) for the variance of all unbiased estimators
e
of .
(b) Find the Cram