Midterm1 Solution

# Midterm1 Solution - Solution for 36217 Wanjie Wang Teacher...

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Unformatted text preview: Solution for 36217 Wanjie Wang Teacher: Jiashun Jin September 30, 2009 If there is any question, please contact me at [email protected] 1. Definitions and expressions (a) the event that stands for ”event A happens but event B does not happen” A ∩ B c or A/B (b) definition of independence P ( A ∩ B ) = P ( A ) P ( B ) (c) The PMF of Poisson( λ ) P ( X = k ) = e- λ λ k k ! 2 True or False (a) T (b) F should be P ( A | B ) = P ( A ) (c) T (d) T (e) F 3. The distribution of random variable X... (a) Find P ( X = 6). With the definition of probability, the sum of probability over universal set Ω is 1. So, P ( X = 6) = 1- P ( X =- 2)- P ( X =- 3)- P ( X = 4) = 1 3 (b) Find the mean E [ X ]. E [ X ] = ∑ k kP ( X = k ) = 1 4 × (- 2) + 1 6 × (- 3) + 1 4 × 4 + 1 3 × 6 = 2 1 (c) Find the variance Var(X). V ar ( X ) = ∑ k ( k- E [ X ]) 2 P ( X = k ) = 1 4 × (- 2- 2) 2 + 1 6 × (- 3- 2) 2 + 1 4 × (4- 2) 2 + 1 3 × (6- 2) 2 = 14 . 5 (d) Find the standard deviation σ X ....
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Midterm1 Solution - Solution for 36217 Wanjie Wang Teacher...

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