Re: Maybe Exponential? check it out
- From: Robert Israel <israel@xxxxxxxxxxxxxxxxxxxxxxxxxxxxx>
- Date: Sun, 04 Nov 2007 15:32:37 -0600
quasi <quasi@xxxxxxxx> writes:
On Sun, 4 Nov 2007 10:39:55 -0800, "Phil Holman"
<piholmanc@yourservice> wrote:
"quasi" <quasi@xxxxxxxx> wrote in message
news:4k2ri39mstgem5sj9sqp10r9ahmpmcbfr1@xxxxxxxxxx
Yeah probably, but enough to know that a rate parameter is missing.
On Sat, 3 Nov 2007 23:35:54 -0700, "Phil Holman"
<piholmanc@yourservice> wrote:
"Craig" <rocketsummerband@xxxxxxxxx> wrote in message
news:25325117.1194131992987.JavaMail.jakarta@xxxxxxxxxxxxxxxxxxxxxxxxx
the time to make a pizza is exponentially distributed with average
mean 6 minutes.
If 250 people want pizza in one week, what is the probability that
AT
LEAST half of them need to wait more than 6 minutes to get their
pizza?
Looks like it might be binomial to me. what do you think?
Would that be exponentially growing or decaying? I think your
problem is incorrectly stated.
Your objection is based on a lack of understanding.
Look up "exponential distribution".
An exponential distribution requires only one parameter. Knowing the
mean is sufficient to uniquely define the distribution. Thus, given
that the time to make a pizza is exponentially distributed with
average time 6 minutes, the distribution is fully specified.
Of course, it may not seem realistic that the time to make a pizza
should be exponentially distributed, but we can simply accept that as
given information. There's no issue with that.
However, there are _other_ aspects of the problem that are far too
vague. For example:
(1) A pizza is only made when a customer arrives?
(2) Do the customers always arrive solo (not in groups)?
(3) Each customer orders a full pizza (not a slice)?
(4) Only one pizza can be made at a time?
(5) Is the pizza shop open 24 hours a day, 7 days a week?
(6) To say 250 customers arrive per week means what -- is that a mean
or an exact amount?
(7) What is the distribution of the customer arrivals? Uniform?
Exponential?
In the absence of further information, we can select default answers
for the above questions, and based on that, we _can_ analyze (by
simulation, if necessary) the OP's question.
But I think the OP should first clarify the model by answering the
above questions.
What I'm pointing out is that the specification of an exponential
distribution with mean 6 minutes for the time to make a pizza -- that
part is fine. The real issue is the vagueness of the problem with
respect to everything else.
It's most likely that the author's intention was to assume that the waiting
times of the 250 customers were independent, and equal to the time to make
their pizzas. Otherwise more information would have to be supplied.
However, it would become an interesting problem if you were to assume that
this was an M/M/1 queue, i.e. customers arrived according to a Poisson
process, and later customers' pizzas aren't started until earlier customers
are served. I don't know how to solve that.
--
Robert Israel israel@xxxxxxxxxxxxxxxxxxxxxxxxxxxxx
Department of Mathematics http://www.math.ubc.ca/~israel
University of British Columbia Vancouver, BC, Canada
.
- Follow-Ups:
- Re: Maybe Exponential? check it out
- From: Craig
- Re: Maybe Exponential? check it out
- References:
- Maybe Exponential? check it out
- From: Craig
- Re: Maybe Exponential? check it out
- From: Phil Holman
- Re: Maybe Exponential? check it out
- From: quasi
- Re: Maybe Exponential? check it out
- From: Phil Holman
- Re: Maybe Exponential? check it out
- From: quasi
- Maybe Exponential? check it out
- Prev by Date: Re: Problem related to a linear regression
- Next by Date: Re: Is a line segment composed of points?
- Previous by thread: Re: Maybe Exponential? check it out
- Next by thread: Re: Maybe Exponential? check it out
- Index(es):
Relevant Pages
|
