Suppose k is a binomial random variable with parameters n and p and let x=(k-np)//sqrt(npq) where q=1-p. If x is of o(n^(1//6)) and there exist some positive numbers A,B and C then show that |(b(k;n,p)sqrt(npq))/(varphi(x))-1| < (A)/(n)+(B|x|^(3))/(sqrtn)+(C|x|)/(sqrtn), where b(k;n,p) is probability mass function of a binomial random variable and varphi(x) is the probability density function of a normal random variable.

Suppose k is a binomial random variable with parameters n and p and let x=(k-np)//sqrt(npq) where q=1-p. If x is of o(n^(1//6)) and there exist some positive numbers A,B and C then show that |(b(k;n,p)sqrt(npq))/(varphi(x))-1| < (A)/(n)+(B|x|^(3))/(sqrtn)+(C|x|)/(sqrtn), where b(k;n,p) is probability mass function of a binomial random variable and varphi(x) is the probability density function of a normal random variable.

Algebra & Trigonometry with Analytic Geometry

13th Edition

ISBN:9781133382119

Author:Swokowski

Publisher:Swokowski

Chapter10: Sequences, Series, And Probability

Section10.8: Probability

Problem 32E

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Question

Q. # 4 Suppose k is a binomial random variable with parameters n and p and let x=(k-np)//sqrt(npq) where q=1-p. If x is of o(n^(1//6)) and there exist some positive numbers A,B and C then show that |(b(k;n,p)sqrt(npq))/(varphi(x))-1| < (A)/(n)+(B|x|^(3))/(sqrtn)+(C|x|)/(sqrtn), where b(k;n,p) is probability mass function of a binomial random variable and varphi(x) is the probability density function of a normal random variable.

Expression, rule, or law that gives the relationship between an independent variable and dependent variable. Some important types of functions are injective function, surjective function, polynomial function, and inverse function.

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