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chap2 prob 13 ans

# chap2 prob 13 ans - School of Mathematics MATH1715...

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Unformatted text preview: School of Mathematics MATH1715: Introduction to Probability Session 2008/2009 Solutions to Homework III H3.1. (a) X x p X ( x ) = 0 . 1 + 0 . 2 + 0 . 15 + 0 . 2 + 0 . 1 + 0 . 15 + 0 . 05 + 0 . 05 = 1 . (b) • P (1 ≤ X ≤ 4) = p X (1) + p X (2) + p X (3) = 0 . 2 + 0 . 1 + 0 . 15 = 0 . 45 . • P ( X is negative ) = p X (- 3) + p X (- 1) = 0 . 1 + 0 . 2 = 0 . 3 . • P ( X ≥ 3 | X > 0) = P ( X ≥ 3 , X > 0) P ( X > 0) = P ( X ≥ 3) P ( X > 0) = = . 15 + 0 . 05 + 0 . 05 . 2 + 0 . 1 + 0 . 15 + 0 . 05 + 0 . 05 = . 25 . 55 = 5 11 . (c) y 1 4 9 25 64 p Y ( y ) . 15 . 4 . 1 . 25 . 05 . 05 (d) To calculate the mean and variance we need to extend the probability distribution tables with two extra rows: x- 3- 1 1 2 3 5 8 p X ( x ) . 1 . 2 . 15 . 2 . 1 . 15 . 05 . 05 xp X ( x )- . 3- . 2 . 2 . 2 . 45 . 25 . 4 x 2 p X ( x ) . 90 . 20 . 2 . 4 1 . 35 1 . 25 3 . 2 y 1 4 9 25 64 p Y ( y ) . 15 . 4 . 1 . 25 . 05 . 05 yp Y ( y ) . 4 . 4 2 . 25 1 . 25 3 . 2 y 2 p Y ( y ) . 4 1 . 6 20 . 25 21 . 25 204...
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chap2 prob 13 ans - School of Mathematics MATH1715...

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