1. A stick of length L is broken at a random point uniformly distributed on the interval [0, L). Twonew 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 = Lc) An experiment consists on breaking sticks of length L independently as described before untilthe longest new stick has length of at least 0.9L. What is the expected number of sticks to bebroken in this experiment.

Here, we are given a stick of length L, which is broken into two parts. The stick is uniform on the…

Answered: A stick of length L is broken at a…

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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Assume that the variables Y1, Y2,... in a compound Poisson process have Bernoulli distribution with parameter p . Show that the process reduces to the Poisson process of parameter λp.
they take samples of 4 fireworks for quality co from and examine them for defects. let X be the number of defective fireworks in the sample of 4.
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Suppose Y is a continuous random variable drawn from the uniform distributionon the interval [3, 4], that is, Y ∼ Uniform([3, 4]). Conditioned on Y = y, a second randomvariable X is drawn from the uniform distribution on the interval [0, y]. What is fX(x), thepdf of X?
A new warehouse is being designed and a decision concerning the number of loading docks is required. There are two models based on truckarrival assumptions for the use of this warehouse, given that loading a truck requires 1 hour. Using the first model, we assume that the warehouse could be serviced by one of the many thousands of independent truckers who arrive randomly to obtain a load for delivery. It is known that, on average, 1 of these trucks would arrive each hour. For the second model, assume that the company hires a fleet of 10 trucks that are assigned full time to shipments from this warehouse. Under that assumption the trucks would arrive randomly, but the probability of any truck arriving during a given hour is 0.1. Obtain the appropriate probability distribution for each of these assumptions and compare the results.
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