hw07 - (b). Problem 3. The length X of a side of a cube has...

Info iconThis preview shows page 1. Sign up to view the full content.

View Full Document Right Arrow Icon
ORIE 360/560 Fall 2007 Assignment 7 Due Tuesday, Oct. 23 at 2:00 pm Please remember to show your work! Please remember to put your section number and net id on the assignment! Problem 1. The number of minutes airline flights are behind schedule is assumed to follow a gamma distribution with shape parameter α = 2 and rate parameter λ = 1 / 4. (a) Find the probability that a flight is at least than 20 minutes late. Hint: recall that if α > 0 is an integer, then Γ( α ) = ( α - 1)! . (b) Use Markov’s inequality to find a bound on the probability from part (a). (c) Use Chebyshev’s inequality to find a bound on the probability from part (a). Problem 2. A fair coin is tossed 1 , 000 times. Let H be the number of heads tossed. (a) Find a and b such that aH + b is approximately distributed as N (0 , 1). (b) Using your answer to part a , approximate the probability that H < 350. (You will need to use Excel or some other software package that can compute the normal cdf.) (c) As in Problem 1, use Markov’s and Chebyshev’s inequalities to find bounds on the probability from part
Background image of page 1
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: (b). Problem 3. The length X of a side of a cube has pdf f X ( x ) = x-2 , for 1 x . Find the pdf of the surface area of the cube. Problem 4. Suppose you can generate iid uniform (0,1) random variables U 1 ,U 2 ,... . Use them to generate n independent Gamma( m, ) random variables, where n and m are positive integers and > 0. Problem 5. A random vector ( X,Y ) has joint pdf f X,Y ( x,y ) = ( e-y if 0 < x < y, otherwise . Find the joint pdf of Z = Y-X and V = X . Are Z and V independent? The following problem is optional for students enrolled in 360, required for students enrolled in 560. Problem 6. A point in the plane is generated at random according to the following scheme. A radius R is generated from the 2 2 distribution. Independently, an angle is generated from the U (0 , 2 ) distribution. Find the joint distribution of X = R cos and Y = R sin ....
View Full Document

This note was uploaded on 11/12/2008 for the course ORIE 360 taught by Professor Ehrlichman during the Fall '07 term at Cornell University (Engineering School).

Ask a homework question - tutors are online