Course1_0501

# Course1_0501 - COURSE 1 MAY 2001 1. The price of an...

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COURSE 1 MAY 2001

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May 2001 7 Course 1 1. The price of an investment at the end of month n is modeled by p n = ne bn where b is a constant. The model predicts that the price at the end of the sixth month is the same as the price at the end of the fifth month. Determine b . (A) 5 ln 6    (B) 55 ln 66 (C) 56 ln 65 (D) 7 ln 6 (E) 6 ln 5
May 2001 8 Course 1 2. A stock pays annual dividends. The first dividend is 8 and each dividend thereafter is 7% larger than the prior dividend. Let m be the number of dividends paid by the stock when the cumulative amount paid first exceeds 500 . Calculate m . (A) 23 (B) 24 (C) 25 (D) 26 (E) 27

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May 2001 9 Course 1 3. The coordinates of an object moving in R 2 are: x = 4 sin 2 t y = 2 t cos t for time t > 0 . Calculate the length of the velocity vector of the object at time t = 2 π . (A) 2 (B) (C) 2 2 + (D) 2 4 + (E) 2 +
May 2001 10 Course 1 4. A company agrees to accept the highest of four sealed bids on a property. The four bids are regarded as four independent random variables with common cumulative distribution function () 13 5 1 sin for 22 2 Fx x x π =+ . Which of the following represents the expected value of the accepted bid? (A) 5/2 3/2 cos xx d x ππ (B) 4 1 1s i n 16 xd x + (C) 4 1 i n 16 d x + (D) 3 1 cos 1 sin 4 d x + (E) 3 1 cos 1 sin 4 x d x +

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May 2001 11 Course 1 5. A company is reviewing tornado damage claims under a farm insurance policy. Let X be the portion of a claim representing damage to the house and let Y be the portion of the same claim representing damage to the rest of the property. The joint density function of X and Y is [] 6 1 ( ) for 0, 1 (, ) 0 otherwise. xy x y fxy −+ > > +< = Determine the probability that the portion of a claim representing damage to the house is less than 0.2 . (A) 0.360 (B) 0.480 (C) 0.488 (D) 0.512 (E) 0.520
May 2001 12 Course 1 6. An insurance company issues life insurance policies in three separate categories: standard, preferred, and ultra-preferred. Of the company’s policyholders, 50% are standard, 40% are preferred, and 10% are ultra-preferred. Each standard policyholder has probability 0.010 of dying in the next year, each preferred policyholder has probability 0.005 of dying in the next year, and each ultra-preferred policyholder has probability 0.001 of dying in the next year. A policyholder dies in the next year. What is the probability that the deceased policyholder was ultra-preferred? (A) 0.0001 (B) 0.0010 (C) 0.0071 (D) 0.0141 (E) 0.2817

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May 2001 13 Course 1 7. A joint density function is given by () for 0 1, 0 1 , 0o t h e r w i s e , kx x y fxy << = where k is a constant. What is Cov( X , Y ) ? (A) 1 6 (B) 0 (C) 1 9 (D) 1 6 (E) 2 3
May 2001 14 Course 1 8. The number of items produced by a manufacturer is given by p = 100 xy , where x is the amount of capital and y is the amount of labor. At a particular point in time: (i) the manufacturer has 2 units of capital; (ii) capital is increasing at a rate of 1 unit per month; (iii) the manufacturer has 3 units of labor; and (iv) labor is decreasing at a rate of 0.5 units per month.

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## This note was uploaded on 03/22/2012 for the course MATH Financial taught by Professor Bruce during the Spring '12 term at CUNY Baruch.

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Course1_0501 - COURSE 1 MAY 2001 1. The price of an...

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