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probability distribution (2).docx

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Department
Statistics
Course
STATS 2B03
Professor
Aaron Childs
Semester
Fall

Description
September 25 , 2012 Stats 2B03: Statistical Methods for Science Probability Distribution (2) Bernouilli process - if x is the number of “successes” in a Bernoulli process, then x is called a binomial r.v. with parameters n and p - example: a multiple choice test has 20 questions, with 5 choices for each question. Suppose that a student guesses on every question, and let x be the # of correct answers. The x is binomial with parameters n=20 and p=⅕. Find the probability of getting: a) exactly 6 correct answers b) pass the test a) P(x:6)=P(C(6)W(14)) = ⅕×⅕×…⅕×⅘×⅘…×⅘ 6 14 = (⅕) (1-⅕) Note =3870 20 nC 6xr  Result: the number of arrangements of x s and n-x F is nc =x , “n choose x” = ( where n!=n(n-1)(n-2)…3×2×1, e.g. 5!=5×4×3×2×1=120 b) P(x≥10) P(x=10)+P(x=11)+…+P(x=20) 10 10 11 9 20 0 =( (⅕) (1-⅕) +( (⅕) (1-⅕) +…+( )(⅕) (1-⅕) =0.0026 Note that P(failing)=1-0.0026=.9974 
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