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Unformatted text preview: Department of Mathematics Name: ________________________________ Poly ID: _______________________________ Instructor's Name: _______________________ Course No:_____________________________ Course Section: _________________________ Homework Section No: ___________________ Willis Thai 3.41 MA2212 HW07 Telephone calls enter a college switchboard at a mean rate of 2/3 call per minute according to a Poisson process. Let X denote the waiting time until the tenth call arrives. (a) What is the pdf of X? { { { {
# {{ # , { { (b) What are the momentgenerating function, mean, and variance of X? H{ {
$ { .
$ % #" $ $ % # % $ { .% $ #" 3.47 The waiting times in minutes until two calls to 911, as reported by the Holland Sentinel on November 13 between noon and midnight, were Could these times represent a random sample from a gamma distribution with ? (a) Compare the distribution and sample means. % (b) Compare the distribution and sample variances. $ $ % J$ (c) Compare W{ { { { {
" $ and J (# J. (# { . {$
$ { with the proportion of times that are less than 35.
#$" % % { { {I { { (d) If possible, make some graphical comparisons. % { $ " %' #$" $ $ #$" Willis Thai MA2212 HW07 with Not possible. My brain does not function well when drawing graphs. It reminds me of Physics lab reports. (e) What is your conclusion? Since % , these times could represent a random sample from a gamma distribution { and {, find constants a and b such that { I{ % W{
$ " '{ #$" 3.410 If X is J I I { { $ # " "' { , I 3.414 Cars arrive at a toll booth at a mean rate of five cars every 10 minutes according to a Poisson process. Find the probability that the toll collector will have to wait longer than 26.30 minutes before collecting the eighth toll. { {
# , $ # { {$" $ { # $ " "' { I{ { { { I{ . { I{ and W{ % I{ . I{ , { { 2 { ,J % 3.51 Let X have the pdf X{Y{ { { { { {I 3 {
{ 3.52 Let X have the pdf X{Y{ { { { { {I 3 {
{ { { $ 3 { YX Y F
Y 3 . Find the pdf of
" % . { { $ 3 { F 3 . Find the pdf of
" $ . 3.53 Let X have a gamma distribution with { { { { { {% {I 3 {
$ and
${ . Determine the pdf of . 3 { 3 " { {% $ Willis Thai { { { {
{ ' MA2212 { { {%
& HW07 { { 3.56 Let X have a logistic distribution with pdf X{Y{ Show that X 3 F H 3 . . FF
" X%Y { X%Y { % " $ {. $ . { { . ' { . Y . has a { { { { { {I 3 {
{ { distribution. { . 3.510 Let X have the uniform distribution {. { { { { I.I
{ $ H  # # . $ {  {$ {. Find the pdf of
" . Since {. { { { { {I 3 { { {I $ 3 { {7{ % % 3 { and { {7{ {, then: % ...
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This note was uploaded on 05/18/2008 for the course MA 2212 taught by Professor Yang during the Fall '08 term at NYU Poly.
 Fall '08
 Yang
 Math

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