advertisement

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. 1 2 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) 3 3. Suppose that the supply function for a product is p = x4 + 1, and the equilibrium price is $2. Find the producer’s surplus. 4 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.