At certain times during the year, a bus company runs a special van holding ten passengers from Iowa City to Chicago. After the opening of sales of the tickets, the time (in minutes) between sales of tickets for the trip has a gamma distribution with
= 3 and = 2
A) Assuming independence, record an integral that gives the probability of being sold out within one hour.
B) Approximate part A using a normal distribution. Is this justified?
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Not really looking for the answer, just need to know where to begin.
Where would I even start with this?
would it be an of a gamma distribution?
P(0 < Z < 60)? whats the N(?,?)
or would I use a Chi-square distribution since is 2 R would be 6...... Kinda lost on where to even begin any help would be appreciated.
UM.... Never used yet, the teacher was out for a while and had a sub teach it he never went over it but im sure im supposed to use it thanks again, can you be my teacher? lol
Im going to look at this tomorrow until I understand it im sure he will ask something like this on the test
I think Mr. F slipped at the point noted above; it is not true that if X and Y are i.i.d. random variables then Pr(X + Y < z) = Pr(2 X < z).
Here is an alternative approach which requires some knowledge of the Gamma distribution; see Gamma distribution - Wikipedia, the free encyclopedia, for example.
If are independent random variables with a Gamma distribution and parameters , then their sum has a Gamma distribution with parameters . So the total time to sell 10 tickets has a Gamma distribution with . Hence the probability of being sold out in 60 minutes is where Y has the Gamma distribution just described. You can find this probability from a table of math functions or you can use something electronic. I used an Excel spreadsheet function, GAMMADIST, to find the probability is about 0.5243.
Quite right. I made the same slip I've often corrected in others. I should have read my own reply in this old thread: http://www.mathhelpforum.com/math-he...a-samples.html. Thanks for the save, awkward.