This preview has intentionally blurred sections. Sign up to view the full version.
View Full Document
Unformatted text preview: 550.420 Introduction to Probability Homework #10
Due November .LO) 2011 1. (2 points) Let. the joint distribution function of X , Y. and Z be given by Rg_y'!z(;17,y. z) = (1 — 9“”)(1 — €42le — EA“) for .131 ,2 > 0. (a) Are X. Y. and Z independent?
(b) Find the joint density function of X, Y. and Z.
(c) Find P[X < Y < Z]. 2. (2 points) Let X1. X2, ..., Xn be a random sample of size n. from a
continuous distribution function F with density function f. (a) Calculate the density function of the sample range R = X0.) — X“). (b) Use (a) to find the density function of the range of 11 random numbers
from (0.1). 3. (2 points} Let X 1. X2. X” be independent random variables from a
Uniform((), 6) distribution. where 9 > 0. Show that. n — 1
ElR] : 71+ 19' where R is the range of the sample of random variables. 1 Hint: Use part. (a) of problem 2. n+1 1H R as an estimator of 6 when it. is Remark: This is the basis for using
unknown. 4. (2 points) Let X. Y. and Z be independent. random variables, each with
mean 0 and variance 1. Calculate 13pm}! + 52V]. 5. (2 points) A company puts ﬁve different. types of prizes into their cereal
boxes‘ one in each box and in equal proportions. If a customer decides to
collect all ﬁve prizes, what is the expected number of the boxes of cereals
that he or she will buy? ...
View
Full Document
 Fall '11
 Wierman

Click to edit the document details