Question

A stick is broken into two pieces, at a uniformly random break point. Find the CDF and average of the length of the longer piece.

Answer 1

P(L ≤ l) =P (1-l ≤ U ≤ l)= l- ( 1 - l ) = 2 l - 1

Explanation:

let assume that stick has length 1.Random variable L that make length of a longer piece and random variable U that mark point .See that L < l means that

U≤ l and 1-U ≤l

P(L ≤ l) =P (1-l ≤ U ≤ l)= l- ( 1 - l ) = 2 l - 1

this means 1-l≤U≤l

so we have

if we have L [1/2,1]

then apply the formula we have E(L)=3/4