DEVELOP.MATH(3 VOLS) CUSTOM-W/MML <IC<
16th Edition
ISBN: 9781323235911
Author: BITTINGER
Publisher: Pearson Custom Publishing
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Chapter J, Problem 90ES
To determine
To calculate: The simplified form of the expression
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B1 The x distribution is a special case of Gamma distribution (not to be confused with gamma
function; see below). The density function of the Gamma distribution with parameters
and k is given by
where
-1
e
-x/0
(x) =
=
г(k) Øk
if x > 0, and
otherwise,
г(k) = √ ₁
k-1-x dx
x' e
is the gamma function.
(a) For every k ≥ 1, 0 > 0, find the mode of the density. Hint: The algebra can be
simplified by appropriate use of logarithms.
~
Now suppose that X1,..., Xn id Exp(\) and that we have a prior belief in A which is
consistent with a prior distribution X. Gamma(a, b), for some a, ß, i.e. the prior density
of is
Baxa-1-BA
T(a)
e
=
so 01/ẞ and k = a.
(b) Write down the likelihood, and show that the posterior distribution for \ is also a
Gamma distribution, but with parameters a +n and B + Σ Xi.
(c) Find the mode of the posterior distribution and examine the behaviour as n → ∞.
Find the differential of the function f(x, y) = 2x² - 2xy – 5y² at the point (-6, -5) using Ax = 0.3
and Ay = 0.05.
dz =
Now find Az and compare it to your answer above
Ax=
Hint: If entering a decimal, round to at least 5 places
Chapter J Solutions
DEVELOP.MATH(3 VOLS) CUSTOM-W/MML <IC<
Ch. J - Find the square roots.
1.
Ch. J - Prob. 2DECh. J - Prob. 3DECh. J - Prob. 4DECh. J - Prob. 5DECh. J - Prob. 6DECh. J - Prob. 7DECh. J - Prob. 8DECh. J - Prob. 9DECh. J - Prob. 10DE
Ch. J - Prob. 11DECh. J - Prob. 12DECh. J - Prob. 13DECh. J - Prob. 14DECh. J - Prob. 15DECh. J - Prob. 16DECh. J - Prob. 17DECh. J - Prob. 18DECh. J - Prob. 19DECh. J - Prob. 20DECh. J - Prob. 21DECh. J - Prob. 22DECh. J - Prob. 23DECh. J - Prob. 24DECh. J - Prob. 25DECh. J - Prob. 26DECh. J - Prob. 27DECh. J - Prob. 28DECh. J - Prob. 29DECh. J - Prob. 30DECh. J - Prob. 31DECh. J - Prob. 32DECh. J - Prob. 33DECh. J - Prob. 34DECh. J - Prob. 35DECh. J - Prob. 36DECh. J - Prob. 37DECh. J - Prob. 38DECh. J - Prob. 39DECh. J - Prob. 40DECh. J - Prob. 41DECh. J - Prob. 42DECh. J - Prob. 43DECh. J - Prob. 44DECh. J - Prob. 45DECh. J - Prob. 46DECh. J - Prob. 47DECh. J - Prob. 48DECh. J - Prob. 49DECh. J - Prob. 50DECh. J - Prob. 51DECh. J - Prob. 52DECh. J - Prob. 53DECh. J - Prob. 54DECh. J - Prob. 55DECh. J - Prob. 56DECh. J - Prob. 57DECh. J - Prob. 58DECh. J - Prob. 59DECh. J - Prob. 60DECh. J - Prob. 61DECh. J - Prob. 62DECh. J - Prob. 63DECh. J - Prob. 64DECh. J - Prob. 65DECh. J - Prob. 66DECh. J - Prob. 1ESCh. J - Prob. 2ESCh. J - Prob. 3ESCh. J - Prob. 4ESCh. J - Prob. 5ESCh. J - Prob. 6ESCh. J - Prob. 7ESCh. J - Prob. 8ESCh. J - Prob. 9ESCh. J - Prob. 10ESCh. J - Prob. 11ESCh. J - Prob. 12ESCh. J - Prob. 13ESCh. J - Prob. 14ESCh. J - Prob. 15ESCh. J - Prob. 16ESCh. J - Prob. 17ESCh. J - Prob. 18ESCh. J - Prob. 19ESCh. J - Prob. 20ESCh. J - Prob. 21ESCh. J - Prob. 22ESCh. J - Prob. 23ESCh. J - Prob. 24ESCh. J - Prob. 25ESCh. J - Prob. 26ESCh. J - Prob. 27ESCh. J - Prob. 28ESCh. J - Prob. 29ESCh. J - Prob. 30ESCh. J - Prob. 31ESCh. J - Prob. 32ESCh. J - Prob. 33ESCh. J - Prob. 34ESCh. J - Prob. 35ESCh. J - Prob. 36ESCh. J - Prob. 37ESCh. J - Prob. 38ESCh. J - Prob. 39ESCh. J - Prob. 40ESCh. J - Prob. 41ESCh. J - Prob. 42ESCh. J - Prob. 43ESCh. J - Prob. 44ESCh. J - Prob. 45ESCh. J - Prob. 46ESCh. J - Prob. 47ESCh. J - Prob. 48ESCh. J - Prob. 49ESCh. J - Prob. 50ESCh. J - Prob. 51ESCh. J - Prob. 52ESCh. J - Prob. 53ESCh. J - Prob. 54ESCh. J - Prob. 55ESCh. J - Prob. 56ESCh. J - e
Rewrite without rational exponents, and...Ch. J - Prob. 58ESCh. J - Prob. 59ESCh. J - Prob. 60ESCh. J - Prob. 61ESCh. J - Prob. 62ESCh. J - Prob. 63ESCh. J - Prob. 64ESCh. J - Prob. 65ESCh. J - Prob. 66ESCh. J - Prob. 67ESCh. J - Prob. 68ESCh. J - Prob. 69ESCh. J - Prob. 70ESCh. J - Prob. 71ESCh. J - Prob. 72ESCh. J - Prob. 73ESCh. J - Prob. 74ESCh. J - Prob. 75ESCh. J - Prob. 76ESCh. J - Prob. 77ESCh. J - Prob. 78ESCh. J - Prob. 79ESCh. J - Prob. 80ESCh. J - Prob. 81ESCh. J - Prob. 82ESCh. J - Prob. 83ESCh. J - Prob. 84ESCh. J - Prob. 85ESCh. J - Prob. 86ESCh. J - Prob. 87ESCh. J - Prob. 88ESCh. J - Prob. 89ESCh. J - Prob. 90ESCh. J - Prob. 91ESCh. J - Prob. 92ESCh. J - Prob. 93ESCh. J - Prob. 94ES
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