exam2 - EECS 501 EXAM#2 Fall 2001 PRINT YOUR NAME HERE...

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EECS 501 EXAM #2 Fall 2001 PRINT YOUR NAME HERE: HONOR CODE PLEDGE: ”I have neither given nor received aid on this exam, nor have I concealed any violations of the honor code.” Open book; SHOW ALL OF YOUR WORK! SIGN YOUR NAME HERE: (30) 1. A fair (Pr[heads]= 1 2 ) coin is flipped n times (independent flips), resulting in k heads. Note: Do not use the Demoivre-Laplace correction in this problem. (5) a. Compute mean E [ k ] and variance σ 2 k as functions of n . (5) b. If n = 1600, compute Pr [790 k 810] (give a specific number). (5) c. If n = 1600, compute the largest b such that Pr [ k b ] 0 . 9. (5) d. Compute a quadratic equation for the smallest n such that Pr [ k 1000] 0 . 95. (5) e. Solve the quadratic equation you computed in (d). What is n ? (5) f. Let e = k n - 1 2 . Compute σ 2 e as a function of n . Compute LIM n →∞ σ 2 e . WRITE YOUR ANSWERS HERE: (a): E [ k ]= σ 2 k = (b): Pr[]= (c): b = (d): (e): n = (f): σ 2 e = LIM n →∞ σ 2 e = 1
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(30) 2. x 1 x 2 x 3 ∼ N 0 0 0 , 2 - 1 - 1 - 1 2 - 1 - 1 - 1 2 .
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