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YoHoJo
10-12-2012, 02:37 AM
Hypogeometric and Poisson distribution questions.
Extreme lost!

Link to assignment:
https://www.dropbox.com/s/zlnh40x72gdqvx1/Case_Study_01%20%281%29.pdf


I know I sound like 1 post nooblet, but if it will help, I'll pay for some assistance <3.

NKN
10-12-2012, 02:41 AM
The transfer of money is only allowed in the Black Market.
Silly mod

Benny
10-12-2012, 06:53 AM
The transfer of money is only allowed in the Black Market.
Silly mod

+1 sir.

In before infraction, suspension and ban.

Lord
10-12-2012, 01:23 PM
Oh my.
This would have been a good opportunity to make some currency,
but unfortunately i've only studied up to Normal Distributions :(

riwu
10-12-2012, 01:31 PM
1a.
Binomial distribution: There are only 2 outcomes: purchase, or dont purchase, and decisions made by every customer is independent of each other (i.e. decision of customer A will not affect that of customer B).

1bi.
48/120 would purchase implies that the probability of a customer purchasing is 48/120=0.4.
Hence X~B(50, 0.4).
P(X=25)=0.040463=0.0405

1bii.
P(X>=25)=1-P(X<=24)=0.0978

1c.
Normal distribution. Key phrase: 'huge database of customers', hence by the central limit theorem, X can be approximate to a normal distribution.

1ci.
E(X)=50*0.4=20
Var(X)=np(1-p)=50*0.4*0.6=12
X~N(20,12)
P(X=25)=0.0406

1cii.
P(X>=25)=0.0745

1d.
This graph should give you an idea of the difference:
http://upload.wikimedia.org/wikipedia/commons/b/b7/Binomial_Distribution.svg

At exact values (part i of qns 1&2), the graph intersect so the ans would be about the same. Normal distribution graph is smoother as it consider the case of decimal value of X as well, while a binomial distribution only considers the integer values of X. Not really sure how to phrase this but you get the rough idea :p

1e.
Let n be the number of customers selected.
X~(n, 0.4)
P(X>20)<=0.01
1-P(X<=18)<=0.01

This will be a long series of algebras so i'd express it in the form of a loop :p
for i:=0 to 18 do
PTotal:=PTotal+(nCi)(0.4^i)(0.6^(n-i)) (formula given in most formula lists)

1-PTotal-0.01<=0
Solve the inequality with a graphic calculator (plot graph and find the x-intercepts).


2a.
Xi~Po(0.7)
P(Xi>=2)=1-P(Xi<=1)=0.156

2b.
E(10Xi)=0.7*10=7

2c.
hmm seems like ans for 2b should be here. What do they mean by 'simulating' in 2b?

2d.
SD=sqd root 7=2.65

2e.
Don't really understand 'simulation', I don't know about 'R Commander' so it may be related to that.

2f.
Expected loss=5^0.7=$3.09 k

2g.
No. The average cost is only ~$3k/year, which is significantly less than the insurance fee of $20k/year. Also from 2a, the probability that the company would pay more than $20k/year (i.e. >=2 earthquakes) is pretty low.

(On an economic point of view, a stable maintenance cost may allow the company to plan and project profits more accurately. It may also be more favorable for small companies, depending on the company's capacity to absorb losses and willingness to take risks, as a devastating year with several earthquakes could cause bankruptcy)

Feel free to ask if you don't understand any part.

Kasi
10-12-2012, 01:41 PM
...

Stats student?!

Turpinator
10-12-2012, 05:08 PM
Well, riwu has said it pretty well. As for your comment on 2e about 'R' and 'R-commander'... R is some stats program that alot of universities use in lower level stats courses. I have used R before when helping a friend, but in my 400 lvl stats class, we do everything by hand. oh joy. <_<
Annnyway.

1d. What riwu is trying to say is that binomial distribution is discrete, meaning the x can only be set integer values from a to b, thus meaning P(X=x) < 0 (where a<X<b and an integer),
whereas with normal distribution is continuous meaning X can really be any value, and therefore P(X=x) = 0.
Discrete CDF are calculated using Sigma/sum of a sequence whereas continuous CDF are calculated using integral.

And, i realize now this is 8 mins late (assuming youre in EST), but better late than never?

cause
10-14-2012, 08:52 PM
Wow nice answer riwu. Btw yoho we must be in the same kind of class. Here's a decent way to distinguish which formula you should use, my prof broke it down like this: (no it's not a rap)

All outcomes have same probability? - uniform
>2 outcomes? - multinomial
2 outcomes:
-time or space interval: (cant remember forgot to write it down)
-1st success: Geometric
-kth success: Negative Binomial
-sample without replacement - Hypergeometric
-A discrete number "4 trees from..." - binomial

Sorry that binomial description is weak.