Business Math (11th Edition)
11th Edition
ISBN: 9780134496436
Author: Cheryl Cleaves, Margie Hobbs, Jeffrey Noble
Publisher: PEARSON
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Chapter 1.1, Problem 23SE
To determine
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optimizaton theory
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 → ∞.
Chapter 1 Solutions
Business Math (11th Edition)
Ch. 1.1 - Prob. 1-1SCCh. 1.1 - Prob. 1-2SCCh. 1.1 - Prob. 1-3SCCh. 1.1 - Prob. 1-4SCCh. 1.1 - Prob. 2-1SCCh. 1.1 - Prob. 2-2SCCh. 1.1 - Prob. 2-3SCCh. 1.1 - Prob. 2-4SCCh. 1.1 - Prob. 3-1SCCh. 1.1 - Prob. 3-2SC
Ch. 1.1 - Prob. 3-3SCCh. 1.1 - Prob. 3-4SCCh. 1.1 - Prob. 3-5SCCh. 1.1 - Prob. 3-6SCCh. 1.1 - Prob. 4-1SCCh. 1.1 - Prob. 4-2SCCh. 1.1 - Prob. 4-3SCCh. 1.1 - Prob. 4-4SCCh. 1.1 - Prob. 1SECh. 1.1 - Prob. 2SECh. 1.1 - Prob. 3SECh. 1.1 - Prob. 4SECh. 1.1 - Prob. 5SECh. 1.1 - Prob. 6SECh. 1.1 - Prob. 7SECh. 1.1 - Prob. 8SECh. 1.1 - Prob. 9SECh. 1.1 - Prob. 10SECh. 1.1 - Prob. 11SECh. 1.1 - Prob. 12SECh. 1.1 - Prob. 13SECh. 1.1 - Prob. 14SECh. 1.1 - Prob. 15SECh. 1.1 - Prob. 16SECh. 1.1 - Prob. 17SECh. 1.1 - Prob. 18SECh. 1.1 - Prob. 19SECh. 1.1 - Prob. 20SECh. 1.1 - Prob. 21SECh. 1.1 - Prob. 22SECh. 1.1 - Prob. 23SECh. 1.1 - Prob. 24SECh. 1.1 - Prob. 25SECh. 1.1 - Prob. 26SECh. 1.2 - Prob. 1-1SCCh. 1.2 - Prob. 1-2SCCh. 1.2 - Prob. 1-3SCCh. 1.2 - Prob. 1-4SCCh. 1.2 - Prob. 1-5SCCh. 1.2 - Prob. 1-6SCCh. 1.2 - Prob. 1-7SCCh. 1.2 - Prob. 1-8SCCh. 1.2 - Prob. 1-9SCCh. 1.2 - Prob. 1-10SCCh. 1.2 - Prob. 1-11SCCh. 1.2 - Prob. 1-12SCCh. 1.2 - Prob. 2-1SCCh. 1.2 - Prob. 2-2SCCh. 1.2 - Prob. 2-3SCCh. 1.2 - Prob. 2-4SCCh. 1.2 - Prob. 2-5SCCh. 1.2 - Prob. 2-6SCCh. 1.2 - Prob. 3-1SCCh. 1.2 - Prob. 3-2SCCh. 1.2 - Prob. 3-3SCCh. 1.2 - Prob. 3-4SCCh. 1.2 - Prob. 3-5SCCh. 1.2 - Prob. 3-6SCCh. 1.2 - Prob. 3-7SCCh. 1.2 - Prob. 3-8SCCh. 1.2 - Prob. 3-9SCCh. 1.2 - Prob. 3-10SCCh. 1.2 - Prob. 4-1SCCh. 1.2 - Prob. 4-2SCCh. 1.2 - Prob. 4-3SCCh. 1.2 - Prob. 4-4SCCh. 1.2 - Prob. 4-5SCCh. 1.2 - Prob. 4-6SCCh. 1.2 - Prob. 4-7SCCh. 1.2 - Prob. 4-8SCCh. 1.2 - Prob. 4-9SCCh. 1.2 - Prob. 4-10SCCh. 1.2 - Prob. 5-1SCCh. 1.2 - Prob. 5-2SCCh. 1.2 - Prob. 5-3SCCh. 1.2 - Prob. 5-4SCCh. 1.2 - Prob. 1SECh. 1.2 - Prob. 2SECh. 1.2 - Prob. 3SECh. 1.2 - Prob. 4SECh. 1.2 - Prob. 5SECh. 1.2 - Prob. 6SECh. 1.2 - Prob. 7SECh. 1.2 - Prob. 8SECh. 1.2 - Prob. 9SECh. 1.2 - Prob. 10SECh. 1.2 - Prob. 11SECh. 1.2 - Prob. 12SECh. 1.2 - Prob. 13SECh. 1.2 - Prob. 14SECh. 1.2 - Prob. 15SECh. 1.2 - Prob. 16SECh. 1.2 - Prob. 17SECh. 1.2 - Prob. 18SECh. 1.2 - Prob. 19SECh. 1.2 - Prob. 20SECh. 1.2 - Prob. 21SECh. 1.2 - Prob. 22SECh. 1.2 - Prob. 23SECh. 1.2 - Prob. 24SECh. 1.2 - Prob. 25SECh. 1.2 - Prob. 26SECh. 1.2 - Prob. 27SECh. 1.2 - Prob. 28SECh. 1.2 - Prob. 29SECh. 1.2 - Prob. 30SECh. 1.2 - Prob. 31SECh. 1.2 - Prob. 32SECh. 1.2 - Prob. 33SECh. 1.2 - Prob. 34SECh. 1.2 - Prob. 35SECh. 1.2 - Prob. 36SECh. 1.2 - Prob. 37SECh. 1.2 - Prob. 38SECh. 1.2 - Prob. 39SECh. 1.2 - Prob. 40SECh. 1.2 - Prob. 41SECh. 1.2 - Prob. 42SECh. 1.2 - Prob. 43SECh. 1.2 - Prob. 44SECh. 1.2 - Prob. 45SECh. 1.2 - Prob. 46SECh. 1.2 - Prob. 47SECh. 1.2 - Prob. 48SECh. 1.2 - Prob. 49SECh. 1.2 - Prob. 50SECh. 1.2 - Prob. 51SECh. 1.2 - Prob. 52SECh. 1.2 - Prob. 53SECh. 1.2 - Prob. 54SECh. 1.2 - Prob. 55SECh. 1.2 - Prob. 56SECh. 1 - Prob. 1ESCh. 1 - Prob. 2ESCh. 1 - Prob. 3ESCh. 1 - Prob. 4ESCh. 1 - Prob. 5ESCh. 1 - Prob. 6ESCh. 1 - Prob. 7ESCh. 1 - Prob. 8ESCh. 1 - Prob. 9ESCh. 1 - Prob. 10ESCh. 1 - Prob. 11ESCh. 1 - Prob. 12ESCh. 1 - Prob. 13ESCh. 1 - Prob. 14ESCh. 1 - Prob. 15ESCh. 1 - Prob. 16ESCh. 1 - Prob. 17ESCh. 1 - Prob. 18ESCh. 1 - Prob. 19ESCh. 1 - Prob. 20ESCh. 1 - Prob. 21ESCh. 1 - Prob. 22ESCh. 1 - Prob. 23ESCh. 1 - Prob. 24ESCh. 1 - Prob. 25ESCh. 1 - Prob. 26ESCh. 1 - Prob. 27ESCh. 1 - Prob. 28ESCh. 1 - Prob. 29ESCh. 1 - Prob. 30ESCh. 1 - Prob. 31ESCh. 1 - Prob. 32ESCh. 1 - Prob. 33ESCh. 1 - Prob. 34ESCh. 1 - Prob. 35ESCh. 1 - Prob. 36ESCh. 1 - Prob. 37ESCh. 1 - Prob. 38ESCh. 1 - Prob. 39ESCh. 1 - Prob. 40ESCh. 1 - Prob. 41ESCh. 1 - Prob. 42ESCh. 1 - Prob. 43ESCh. 1 - Prob. 44ESCh. 1 - Prob. 45ESCh. 1 - Prob. 46ESCh. 1 - Prob. 47ESCh. 1 - Prob. 48ESCh. 1 - Prob. 49ESCh. 1 - Prob. 50ESCh. 1 - Prob. 51ESCh. 1 - Prob. 52ESCh. 1 - Prob. 53ESCh. 1 - Prob. 54ESCh. 1 - Prob. 55ESCh. 1 - Prob. 56ESCh. 1 - Prob. 57ESCh. 1 - Prob. 58ESCh. 1 - Prob. 59ESCh. 1 - Prob. 60ESCh. 1 - Prob. 61ESCh. 1 - Prob. 62ESCh. 1 - Prob. 63ESCh. 1 - Prob. 64ESCh. 1 - Prob. 65ESCh. 1 - Prob. 66ESCh. 1 - Prob. 67ESCh. 1 - Prob. 68ESCh. 1 - Prob. 69ESCh. 1 - Prob. 70ESCh. 1 - Prob. 71ESCh. 1 - Prob. 72ESCh. 1 - Prob. 73ESCh. 1 - Prob. 74ESCh. 1 - Prob. 75ESCh. 1 - Prob. 76ESCh. 1 - Prob. 77ESCh. 1 - Prob. 78ESCh. 1 - Prob. 79ESCh. 1 - Prob. 80ESCh. 1 - Prob. 81ESCh. 1 - Prob. 82ESCh. 1 - Prob. 83ESCh. 1 - Prob. 84ESCh. 1 - Prob. 85ESCh. 1 - Prob. 86ESCh. 1 - Prob. 87ESCh. 1 - Prob. 88ESCh. 1 - Prob. 89ESCh. 1 - Prob. 1PTCh. 1 - Prob. 2PTCh. 1 - Prob. 3PTCh. 1 - Prob. 4PTCh. 1 - Prob. 5PTCh. 1 - Prob. 6PTCh. 1 - Prob. 7PTCh. 1 - Prob. 8PTCh. 1 - Prob. 9PTCh. 1 - Prob. 10PTCh. 1 - Prob. 11PTCh. 1 - Prob. 12PTCh. 1 - Prob. 13PTCh. 1 - Prob. 14PTCh. 1 - Prob. 15PTCh. 1 - Prob. 16PTCh. 1 - Prob. 17PTCh. 1 - Prob. 18PTCh. 1 - Prob. 19PTCh. 1 - Prob. 20PTCh. 1 - Prob. 21PTCh. 1 - Prob. 22PTCh. 1 - Prob. 23PTCh. 1 - Prob. 24PTCh. 1 - Prob. 25PTCh. 1 - Prob. 26PTCh. 1 - Prob. 27PTCh. 1 - Prob. 28PTCh. 1 - Prob. 29PTCh. 1 - Prob. 30PTCh. 1 - Prob. 31PTCh. 1 - Prob. 32PTCh. 1 - Prob. 1CTCh. 1 - Prob. 2CTCh. 1 - Prob. 3CTCh. 1 - Prob. 4CTCh. 1 - Prob. 5CTCh. 1 - Prob. 6CTCh. 1 - Prob. 7CTCh. 1 - Prob. 8CTCh. 1 - Prob. 9CTCh. 1 - Prob. 10CTCh. 1 - Prob. 11CTCh. 1 - Prob. 12CTCh. 1 - Prob. 1CPCh. 1 - Prob. 2CPCh. 1 - Prob. 1CS1Ch. 1 - Prob. 2CS1Ch. 1 - Prob. 3CS1Ch. 1 - Prob. 1CS2Ch. 1 - Prob. 2CS2Ch. 1 - Prob. 3CS2Ch. 1 - Prob. 1CS3Ch. 1 - Prob. 2CS3Ch. 1 - Prob. 3CS3Ch. 1 - Prob. 4CS3Ch. 1 - Prob. 5CS3
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