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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Given P (X) = 0.4, P (Y) = 0.4 and P (X/Y') = 0.25. i) Find the probability that the event Y does not occur. ii) Draw a contingency table to represent the events above. iii) Find P (X UY).
Suppose claim amounts at a health insurance company are independent of one another. In the first year calim amounts are modeled by a gamma random variable X with alpha=40, and beta=3. In the second year, individual claim amounts are modeled by random variable Y=1.05X+3. Let W be the average of 30 claim amounts in year two set up the equation to model the random variable W. a) Find the moment generating function of W b) Based on moment generating function of W is W also a gamma distribution? if so what are the parameters? c) Find the approximate probability that W is between 125$ and 130$.
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1. If X,X2, .,X, forms a random sample of size n from a population with pdf f(x; 0,8) = for x>0 elsewhere Find estimators for 8 and 0 by the method of moments.
Let X.,X,"(4,0²). Consider the fotlowing estimators of u A, =(X+ Xs + X, + X10) A = (X2+ X, +Xp). Then (a) A, is more efficient than Az (b iz is more efficient than i (e) Can't deside (d) None
4. A particle moves on the x- axis starting at x = 0. With equal probability, the particle moves to the left or right one unit. Let X denote the position on the x- axis after four moves. (a) Find px(x). Notice that X can take on -4,-2,0, 2, 4. Fill out the table below. xPx(x) (b) What is the expected position of the particle after four moves. That is, compute E(X). Express your answer as a fraction in lowest terms.
Suppose we choose arbitrarily a point from the square with corners at(2,1), (3,1), (2,2), and (3,2). The random variable A is the area of the trianglewith its corners at (2,1), (3,1), and the chosen point. Compute E[A].
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