MATH 1100: QUANTITATIVE ANALYSIS
TEST #5 (VERSION A)
Name:
This test has 5 pages and 5 problems.
No calculators are allowed. You are permitted only a pencil or pen. Work out
everything as far as you can before making decimal approximations.
1. Suppose that a business has continuous income stream with an annual rate
of flow at time t given by f (t) = 10000. The interest rate is r = 10%,
compounded continuously. Find the capital value of the income stream.
Date: November 16, 2001.
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MATH 1100: QUANTITATIVE ANALYSIS
TEST #5 (VERSION A)
2. Suppose that
(
ce−kx
f (x) =
0
if x > 0
otherwise
where k > 0. What must the value of c be (in terms of k) so that f (x) is a
probability density function?
MATH 1100: QUANTITATIVE ANALYSIS
TEST #5 (VERSION A)
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3. Suppose that the supply function for a product is p = x4 + 1, and the
equilibrium price is $2. Find the producer’s surplus.
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MATH 1100: QUANTITATIVE ANALYSIS
TEST #5 (VERSION A)
4. Suppose that
(
f (x) =
4
9π
0
√
9 − x2
if 0 < x < 3
otherwise.
Find the mean value of a random variable with f (x) as probability density
function.
MATH 1100: QUANTITATIVE ANALYSIS
TEST #5 (VERSION A)
5
5. Using n rectangles of width 1/n whose left shoulder touches the graph of
f (x) = 2x, approximate the area under the graph of f (x) between x = 0
and x = 1. You might need to know that
n
X
1=n
k=1
n
X
k=1
k = n(n + 1)/2.