Contemporary Mathematics for Business and Consumers
7th Edition
ISBN: 9781285189758
Author: Robert Brechner, George Bergeman
Publisher: Cengage Learning
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Chapter 20.II, Problem 3RE
To determine
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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 20 Solutions
Contemporary Mathematics for Business and Consumers
Ch. 20.I - Techron Industries, Inc., has 1,400,000 shares of...Ch. 20.I - Prob. 2TIECh. 20.I - Prob. 3TIECh. 20.I - Prob. 4TIECh. 20.I - Bentley Systems. Inc., paid a dividend of $0.68...Ch. 20.I - Prob. 6TIECh. 20.I - You purchase 225 shares of Gulfstream Industries...Ch. 20.I - Prob. 1RECh. 20.I - Prob. 2RECh. 20.I - Prob. 3RE
Ch. 20.I - Prob. 4RECh. 20.I - Prob. 5RECh. 20.I - Prob. 6RECh. 20.I - Prob. 7RECh. 20.I - Prob. 8RECh. 20.I - Prob. 9RECh. 20.I - Prob. 10RECh. 20.I - Prob. 11RECh. 20.I - Prob. 12RECh. 20.I - Prob. 13RECh. 20.I - Prob. 14RECh. 20.I - Prob. 15RECh. 20.I - Prob. 16RECh. 20.I - Prob. 17RECh. 20.I - Prob. 18RECh. 20.I - Prob. 19RECh. 20.I - Calculate the total cost, proceeds, and gain (or...Ch. 20.I - Prob. 21RECh. 20.I - Prob. 22RECh. 20.I - Prob. 23RECh. 20.I - Prob. 24RECh. 20.I - Prob. 25RECh. 20.I - Prob. 26RECh. 20.I - 27. Apex Developers. Inc., has 1,800,000 shares of...Ch. 20.I - Prob. 28RECh. 20.I - 29. You purchase 650 shares of Sunrise Electric...Ch. 20.I - Though investing all at once works best when stock...Ch. 20.II - Using Exhibit 20-5. Corporate Bond Quotation...Ch. 20.II - Prob. 9TIECh. 20.II - Prob. 10TIECh. 20.II - Prob. 11TIECh. 20.II - Prob. 1RECh. 20.II - Prob. 2RECh. 20.II - Prob. 3RECh. 20.II - Prob. 4RECh. 20.II - Prob. 5RECh. 20.II - Prob. 6RECh. 20.II - Prob. 7RECh. 20.II - Prob. 8RECh. 20.II - Prob. 9RECh. 20.II - Prob. 10RECh. 20.II - Calculate the accrued interest and the total...Ch. 20.II - Calculate the accrued interest and the total...Ch. 20.II - Prob. 13RECh. 20.II - Prob. 14RECh. 20.II - Prob. 15RECh. 20.II - Prob. 16RECh. 20.II - Prob. 17RECh. 20.II - Prob. 18RECh. 20.II - Prob. 19RECh. 20.II - Prob. 20RECh. 20.II - Prob. 21RECh. 20.II - Prob. 22RECh. 20.II - Prob. 23RECh. 20.II - Prob. 24RECh. 20.II - Prob. 25RECh. 20.III - Using Exhibit 20-6, Mutual Fund Quotation Table,...Ch. 20.III - Prob. 13TIECh. 20.III - Prob. 14TIECh. 20.III - Prob. 15TIECh. 20.III - Prob. 16TIECh. 20.III - Prob. 1RECh. 20.III - Prob. 2RECh. 20.III - Prob. 3RECh. 20.III - Prob. 4RECh. 20.III - Prob. 5RECh. 20.III - Prob. 6RECh. 20.III - Prob. 7RECh. 20.III - Prob. 8RECh. 20.III - Prob. 9RECh. 20.III - Prob. 10RECh. 20.III - Prob. 11RECh. 20.III - Prob. 12RECh. 20.III - Prob. 13RECh. 20.III - Prob. 14RECh. 20.III - Prob. 15RECh. 20.III - Prob. 16RECh. 20.III - Prob. 17RECh. 20.III - Prob. 18RECh. 20.III - Prob. 19RECh. 20.III - Prob. 20RECh. 20.III - Prob. 21RECh. 20.III - Prob. 22RECh. 20.III - Calculate the total cost, proceeds, total gain (or...Ch. 20.III - Prob. 24RECh. 20.III - Prob. 25RECh. 20.III - Prob. 26RECh. 20.III - Prob. 27RECh. 20.III - Prob. 28RECh. 20.III - Prob. 29RECh. 20.III - BUSINESS DECISION: CAPITAL GAINS
30. There are...Ch. 20 - Prob. 1CRCh. 20 - Prob. 2CRCh. 20 - Prob. 3CRCh. 20 - Prob. 4CRCh. 20 - Prob. 5CRCh. 20 - Prob. 6CRCh. 20 - Prob. 7CRCh. 20 - A _____ is a loan, or an IOU, in the form of an...Ch. 20 - Prob. 9CRCh. 20 - 10. Write the formula used to calculate the...Ch. 20 - Prob. 11CRCh. 20 - Prob. 12CRCh. 20 - Prob. 13CRCh. 20 - Prob. 14CRCh. 20 - Prob. 1ATCh. 20 - Prob. 2ATCh. 20 - Prob. 3ATCh. 20 - Prob. 4ATCh. 20 - Prob. 5ATCh. 20 - Prob. 6ATCh. 20 - Prob. 7ATCh. 20 - Prob. 8ATCh. 20 - Prob. 9ATCh. 20 - Prob. 10ATCh. 20 - Prob. 11ATCh. 20 - Prob. 12ATCh. 20 - Calculate the total cost, proceeds and gain (or...Ch. 20 - Prob. 14ATCh. 20 - Prob. 15ATCh. 20 - 16. The board of directors of Micro-Fine...Ch. 20 - Prob. 17ATCh. 20 - Prob. 18ATCh. 20 - 19. You purchase 350 shares of Universal Metals...Ch. 20 - Prob. 20ATCh. 20 - Prob. 21ATCh. 20 - Prob. 22ATCh. 20 - Prob. 23ATCh. 20 - Prob. 24ATCh. 20 - Prob. 25ATCh. 20 - Calculate the accrued interest and the total...Ch. 20 - Prob. 27ATCh. 20 - Prob. 28ATCh. 20 - Prob. 29ATCh. 20 - Prob. 30ATCh. 20 - Prob. 31ATCh. 20 - Prob. 32ATCh. 20 - Prob. 33ATCh. 20 - 34. On May 1. Emerson Fast bought 10 Manitoba...Ch. 20 - Prob. 35ATCh. 20 - Prob. 36ATCh. 20 - Prob. 37ATCh. 20 - Prob. 38ATCh. 20 - Prob. 39ATCh. 20 - Prob. 40ATCh. 20 - Prob. 41ATCh. 20 - Prob. 42ATCh. 20 - Prob. 43ATCh. 20 - Prob. 44ATCh. 20 - Prob. 45ATCh. 20 - Prob. 46ATCh. 20 - Prob. 47ATCh. 20 - Prob. 48ATCh. 20 - Prob. 49AT
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