HW4_123_solution

# HW4_123_solution - Solutions to HW4 Problem 1(1 Yes With...

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Solutions to HW4 Problem 1 (1) Yes. With n=20 and p=0.3 (2) P ( Y = 5) = P ( Y < = 5) - P ( Y < = 4) = 0 . 416 - 0 . 238 = 0 . 178 (3) P ( Y < = 5) = 0 . 416 (4) Compute P ( Y = Y i ) for all possible Y i (that is, all integers from 0 to 20) ... P ( Y = 5) = 0 . 178 P ( Y = 6) = P ( Y < = 6) - P ( Y < = 5) = 0 . 608 - 0 . 416 = 0 . 192 P ( Y = 7) = P ( Y < = 7) - P ( Y < = 6) = 0 . 772 - 0 . 608 = 0 . 164 ... and so on. You will Fnd that P(Y=6) is the largest (i.e. Y=6 is most probable). Problem 2 (4.94) X: the rating. X is normal with mean 605 ( μ ) and standard deviation 185 ( σ ) (1) P (500 < X < 700) = P ( 500 - μ σ < X - μ σ < 700 - μ σ ) = P ( - 0 . 5676 < X - μ σ < 0 . 5135) = P (0 < X - μ σ < 0 . 5676) + P (0 < X - μ σ < 0 . 5135) = 0 . 2157 + 0 . 1950 = 0 . 4107 (2) P (400 < X < 500) = P ( 400 - μ σ < X - μ σ < 500 - μ σ ) = P ( - 1 . 108 < X - μ σ < - 0 . 5676) = P (0 < X - μ σ < 1 . 108) - P (0 < X - μ σ < 0 . 5676) = 0 . 3665 - 0 . 2157 = 0 . 1508 1

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(3) P ( X < 850) = P ( X - μ σ < 850 - μ
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## This note was uploaded on 11/14/2011 for the course ECON UA.18.1-01 taught by Professor Romanfrydman during the Fall '11 term at NYU.

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HW4_123_solution - Solutions to HW4 Problem 1(1 Yes With...

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