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t2f07solns[1]

# t2f07solns[1] - 1 NAME ISyE 3770 Solutions Test 2a Fall...

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1 NAME ISyE 3770 Solutions — Test 2 a — Fall 2007 This test is 80 minutes long. You are allowed one cheat sheet. Do not look at or start the test until you are told to do so. When we ask you to return the test, stop immediately, hand the test in, and do not utter a word to anyone. Do not show any work other than your answers on this sheet. Good luck! Put your nice, simple answers here... 1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11. 12. 13. 14. 15. 16. 17. 18. 19. 20. 21. 22. 23. 24. 25.

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2 1. What does the “m” in “p.m.f.” mean? Solution: mass. 2. Suppose X has p.d.f. f ( x ) = x 2 , 0 x c . Find c . Solution: R c 0 f ( x ) dx = 1 implies c = 3 1 / 3 . 3. Suppose that X is discrete with f ( - 2) = 0 . 2, f (0) = 0 . 5, and f (4) = 0 . 3. Find F (1 . 5), where F ( x ) is the c.d.f. of X . Solution: F (1 . 5) = P ( X 1 . 5) = f ( - 2) + f (0) = 0 . 7 . 4. Suppose X has p.d.f. f ( x ) = 2 x , 0 x 1. Find P (3 / 4 X 5 / 4). Solution: P (3 / 4 X 5 / 4) = P (3 / 4 X 1) = R 1 3 / 4 2 x dx = 7 / 16. 5. Suppose X has p.d.f. f ( x ) = 2 x , 0 x 1. Find P (0 X 1 / 2 | 1 / 4 X 3 / 4). Solution: P (0 X 1 / 2 | 1 / 4 X 3 / 4) = P (0 X 1 / 2 1 / 4 X 3 / 4) P (1 / 4 X 3 / 4) = P (1 / 4 X 1 / 2) P (1 / 4 X 3 / 4) = R 1 / 2 1 / 4 f ( x ) dx R
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