Homework 7 Solutions
University of Massachusetts Amherst
Math 397A
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n
1. The joint density function, f (:0, y)
giVen by
Calculate c.
2. The joint pdf
>for0<y<rcr<land00
(a) C
(b) Pr(X + Y S 1)
(c) P7"(X2 ~lY2 g 1)
(d) flele) '
(e) EiXlY = y)-
3. X and Y are indepe
fx(93) = for O < a: < 5 an
for0<_y<3.
(a) Find PT(X > Y).
Homework 1: Due 1/29
University of Massachusetts Amherst
Math 397A
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Indicate your answer by circling it. You do not have to show work, you should keep
Midterm Solutions
University of Massachusetts Amherst
Math 397A
(1) A fair coin is tossed. If a head occurs, 1 fair die is rolled; if a tail occurs, 2 fair dice are
rolled. If Y is the total on the die or dice, then Pr(Y = 5) =
(A)
1
9
(B)
1
18
(C)
5
36
(
Practice Midterm
University of Massachusetts Amherst
Math 397A
(1) An insurance company examines its pool of auto insurance customers and gathers the
following information:
(a) All customers insure at least one car.
(b) 64% of the customers insure more th
Quiz 8
University of Massachusetts Amherst
Math 397A
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Show your work: there are opportunities for partial credit.
(1) A charity receives 2025 contribu
Quiz 7 Solutions
University of Massachusetts Amherst
Math 397A
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(1) Let X and Y be random
Quiz 6 Solutions
University of Massachusetts Amherst
Math 397A
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(1) The distribution of Y
Quiz 4
University of Massachusetts Amherst
Math 397A
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(1) Let the random variable X have m
Homework 2: Due 2/5
University of Massachusetts Amherst
Math 397A
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Homework 5
University of Massachusetts Amherst
Math 397A
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Homework 9
University of Massachusetts Amherst
Math 397A
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Homework 10 / Extra Credit
University of Massachusetts Amherst
Math 397A
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Homework 7
University of Massachusetts Amherst
Math 397A
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Homework 8
University of Massachusetts Amherst
Math 397A
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Homework 3: Due 2/14
University of Massachusetts Amherst
Math 397A
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Homework 4
University of Massachusetts Amherst
Math 397A
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Homework 6
University of Massachusetts Amherst
Math 397A
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Quiz 5 Solutions
University of Massachusetts Amherst
Math 397A
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(1) An actuary has discove
Quiz 3 Solutions
University of Massachusetts Amherst
Math 397A
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(1) Let X be a random vari
Quiz 2 Solutions
University of Massachusetts Amherst
Math 397A
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(1) Ten percent of a compa
Homework 9 Solutions
University of Massachusetts Amherst
Math 397A
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Homework 10 Solutions
University of Massachusetts Amherst
Math 397A
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Homework 8 Solutions
University of Massachusetts Amherst
Math 397A
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Homework 6 Solutions
University of Massachusetts Amherst
Math 397A
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Homework 4
University of Massachusetts Amherst
Math 397A
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Homework 5 Solutions
University of Massachusetts Amherst
Math 397A
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Homework 3 Solutions
University of Massachusetts Amherst
Math 397A
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