mt2sol - York University MATH 2030 3.0AF (Elementary...

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York University MATH 2030 3.0AF (Elementary Probability) Midterm 2 - Corrected Solutions November 7, 2007 NAME: STUDENT NUMBER: You have 50 minutes to complete the examination. There are 5 pages, containing 5 questions and a Normal table. You may bring one letter-sized two-sided formula sheet to the exam. No other books or notes may be used. You may use a calculator. Show all your work, and explain or justify your solutions to the extent possible. You may leave numerical answers unsimpliﬁed, and you do not have to interpolate when using a normal table. Use the back of your page if you run out of room. 1. A discrete random variable X has the following distribution: x -1 0 2 4 5 P ( X = x ) 0.2 0.1 0.3 c 0.2 All other values have probability 0 of occurring. (a) [5] Find c , explaining what properties you use to reach your conclusion. (b) [5] Find P ( X 3). (c) [5] Find E [ X ]. Solution: (a) P (Ω) = 1, so 1 = 0 . 2 + 0 . 1 + 0 . 3 + c + 0 . 2 = 0 . 8 + c and hence c = 0 . 2 (b) P ( X 3) = P ( X = - 1) + P ( X = 0) + P ( X = 2) = 0 . 2 + 0 . 1 + 0 . 3 = 0 . 6 (c) E [ X ] = x · P ( X = x ) = ( - 1) × 0 . 2+0 × 0 . 1+2 × 0 . 3+4 × 0 . 2+5 × 0 . 2 = 2 . 2 1

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This note was uploaded on 12/11/2010 for the course MATH MATH 2030 taught by Professor Sikh during the Winter '09 term at York University.

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mt2sol - York University MATH 2030 3.0AF (Elementary...

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