no A.I. generated answer or downvote
Exercise 24 (#5.51). Let Fn be the empirical distribution based on a random sample of size n from
a distribution F on R having Lebesgue density f. Let n(t) be the Lebesgue density of the p th
sample quantile Fn1(p). Prove that n(t)=n(n1lp1)[F(t)]lp1[1F(t)]nlpf(t), where lp=np if np is an
integer and lp=1+ the integer part of np if np is not an integer, by (i) using the fact that nFn(t) has a
binomial distribution; (ii) using the fact that Fn1(p)=cnpX(mp)+(1cnp)X(mp+1), where X(j) is the j th
order statistic, mp is the integer part of np,cnp=1 if np is an integer, and cnp=0 if np is not an
integer..
How to Manage Notification Preferences in the Odoo 17
no AI generated answer or downvote Exercise 24 551 Le.pdf
1. no A.I. generated answer or downvote
Exercise 24 (#5.51). Let Fn be the empirical distribution based on a random sample of size n from
a distribution F on R having Lebesgue density f. Let n(t) be the Lebesgue density of the p th
sample quantile Fn1(p). Prove that n(t)=n(n1lp1)[F(t)]lp1[1F(t)]nlpf(t), where lp=np if np is an
integer and lp=1+ the integer part of np if np is not an integer, by (i) using the fact that nFn(t) has a
binomial distribution; (ii) using the fact that Fn1(p)=cnpX(mp)+(1cnp)X(mp+1), where X(j) is the j th
order statistic, mp is the integer part of np,cnp=1 if np is an integer, and cnp=0 if np is not an
integer.
![no A.I. generated answer or downvote
Exercise 24 (#5.51). Let Fn be the empirical distribution based on a random sample of size n from
a distribution F on R having Lebesgue density f. Let n(t) be the Lebesgue density of the p th
sample quantile Fn1(p). Prove that n(t)=n(n1lp1)[F(t)]lp1[1F(t)]nlpf(t), where lp=np if np is an
integer and lp=1+ the integer part of np if np is not an integer, by (i) using the fact that nFn(t) has a
binomial distribution; (ii) using the fact that Fn1(p)=cnpX(mp)+(1cnp)X(mp+1), where X(j) is the j th
order statistic, mp is the integer part of np,cnp=1 if np is an integer, and cnp=0 if np is not an
integer.](https://image.slidesharecdn.com/noaigeneratedanswerordownvoteexercise24551le-230318145646-8de6da53/85/no-AI-generated-answer-or-downvote-Exercise-24-551-Le-pdf-1-320.jpg)
