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A stick of length L is broken at a random point uniformly distributed on the interval [0, L]. Two new sticks are formed. a) If X denotes the length of the longest new stick, calculate E(X) and V(X) b) If Y denotes the length of the shortest new stick, calculate E(Y) and V(Y) Hint: X+Y = L c) An experiment consists on breaking sticks of length L independently as described before until the longest new stick has length of at least 0.9L. What is the expected number of sticks to be broken in this experiment.

A stick of length L is broken at a random point uniformly distributed on the interval [0, L]. Two new sticks are formed. a) If X denotes the length of the longest new stick, calculate E(X) and V(X) b) If Y denotes the length of the shortest new stick, calculate E(Y) and V(Y) Hint: X+Y = L c) An experiment consists on breaking sticks of length L independently as described before until the longest new stick has length of at least 0.9L. What is the expected number of sticks to be broken in this experiment.

MATLAB: An Introduction with Applications
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
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1. A stick of length L is broken at a random point uniformly distributed on the interval [0, L). Two new sticks are formed. a) If X denotes the length of the longest new stick, calculate E(X) and V(X) b) If Y denotes the length of the shortest new stick, calculate E(Y) and V(Y) Hint: X +Y = L c) An experiment consists on breaking sticks of length L independently as described before until the longest new stick has length of at least 0.9L. What is the expected number of sticks to be broken in this experiment.
Transcribed Image Text:1. A stick of length L is broken at a random point uniformly distributed on the interval [0, L). Two new sticks are formed. a) If X denotes the length of the longest new stick, calculate E(X) and V(X) b) If Y denotes the length of the shortest new stick, calculate E(Y) and V(Y) Hint: X +Y = L c) An experiment consists on breaking sticks of length L independently as described before until the longest new stick has length of at least 0.9L. What is the expected number of sticks to be broken in this experiment.
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