STAT 754 Homework 9 (Due Wednesday, April 14)
SPRING 2010
. Suppose that X1, . . . ,Xn form a random sample from a normal distrib—
ution with an unknown mean 6 and a given variance 02. Suppose that
the following hypotheses are to be tested:
H0:0260H116<60
STAT 754 Homework 6 (Due Wednesday, March 3)
SPRING 2010
1. Suppose X1, . . . ,Xn are i.i.d. random variables having a normal dis—
tribution with known mean ,u and unknown variance 6. Let the prior
distribution of 6 have the following pdf:
M6) — 5a 6ﬁia
STAT 754 Homework 8 (Due Wednesday, April 7)
SPRING 2010
1. Let n denote the true mean score on‘ a certain type of test. Consider
the problem of testing H0 : a = 80 versus H1 : n > 80 based on a
sample of size n from a normal population with (7 = 6.
(a) I
STAT 754 Homework 7 (Due Wednesday, March 24)
SPRING 2010
‘ Suppose X1, . . . 7Xn are i.i.d. random variables having a distribution
speciﬁed below. In each case use the factorization criterion to find
sufﬁcient statistic.
(a) Gamma distribution unknown 01
1.
3.
STAT 754 Homework 4 (Due Wednesday, February 17)
SPRING 2010
A random sample X1, . . . ,Xn is taken from a normal distribution with
2
an unknown mean u and given variance 0 .
(a) Please explain how_to derive a (1 ~ d)100% conﬁdence interval for
,u u
STAT 754 Homework 1
SPRING 2010
Due Wednesday, February 3
1. Let X and Y have a joint continuous distribution on R2 given by the
PDF f(sc,y) = or for E D and f(:r,y) : 0 otherwise, where
D={(a:,y):r>0,y>0,93+y<1}.
(a) Determine the constant c.
(b) Determi
STAT 754 Homework 2
SPRING 2010
Due Wednesday, February 10
Consider the function
1
: 27TIZ’1/26";(X—M)/2—1(X_H), X 2 (331,332) 6 R2)
where a :(u1,ag)’, —00 < rim/L2 < oo,
2
E _ 01 palm
— 2
p0102 02 ’
01, 02 > 0, —1 < p < 1, and }E[ denotes the determinan
STAT 754 Homework 3
SPRING 2010
Due Wednesday, February 6
1. Section 7.2, No 10
2. Suppose that the ﬁve random variables X1, X2, . . . ,X5 are i.i.d. and
that each has a standard normal distribution. Determine a constant c
such that the random variable
C(
STAT 754 Homework 5 (Due Wednesday, February 24)
SPRING 2010
1. Suppose X1, . . . ,Xn are i.i.d. random variables from the distribution
having the following probability density function:
f(o:[6) = e‘<m’9), 6 g x < oo, —oo < 6 < 00.
Find the MLE of 6.
2. S
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MATH 754 Homework 10
Due Wednesday, April 28
SPRING 2010
1. Section 9.1, No. 5
2. Section 9.1, No. 7
3. Section 9.2, No. 2
4. Let n1, . . . ,nk be a vector of observations representing a multinomial
random variable with parameters n and p1, . . . , pk. Sh