Probability and Statistical Inference (9th Edition)
9th Edition
ISBN: 9780321923271
Author: Robert V. Hogg, Elliot Tanis, Dale Zimmerman
Publisher: PEARSON
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Textbook Question
Chapter 8.1, Problem 7E
Vitamin B6 is one of the vitamins in a multiple vitamin pill manufactured by a pharmaceutical company. The pills are produced with a
A consumer group suspects that
(a) Define a critical region to test
(b) If the 20 pills yielded a mean of
(c) What is the approximate p-value of this test?
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-xx0.
B2 If Xfx(x) find the MGF in the case that
fx(x) =
-
1
28
exp{-|x − a\/ẞ},
Use the MGF to compute E(X) and Var(X).
B3 Consider X ~ Bern(p)
(a) Find Mx(t), the moment generating function of X.
iid
(b) If X1,..., Xn
Bern(p), find the MGF, say My (t) of
n
Y =
ΣΧ
(c) Using the fact that
i=1
n
lim (1
(1+2)"=
N→X
= e²
find limn→∞ My (t) in the case that p satisfies limn→∞ np = λ, say.
(d) State the distribution of Y in the case that n is not large, and the distribution of Y in
the limiting case described in the question.
B1 The density of the x2 distribution is given in the notes as
1
F(§)2/2
(x)=()2/21
x/2-1/2, if x > 0, and
e
where I(t)=√xt-¹e dx is the gamma function.
otherwise,
Find the point at which o(a) has its maximum, i.e. find arg max, o, (x)
Chapter 8 Solutions
Probability and Statistical Inference (9th Edition)
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