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## statistics cheat sheet

Sumemr 2008 page compiled on July 2, 2015 at 6:07pm

problem: phone calls received at rate per hr. If person wants to take 10 min shower, what is probability a phone will ring during that time?

answer: ﬁrst change to , now we want but , but remember, we are using , so so so , so change the phone will ring.

How long can shower be if they wish probability of receiving no phone calls to be at most 0.5? hence , so minutes

To ﬁnd quantile, say , ﬁrst ﬁnd an expression for as function of , then solve for in For median, solve for in properties of CDF: 1. Show for all Do this by showing , and show limit as and limit as . And properties of pdf:

1.
piecewise continuous
2.
pdf 3. remember The geometric distribution is the only discrete memoryless random distribution. It is a discrete analog of the exponential distribution. continuous

Some relations Geometric sum if , then if the sum is from 1 then if , then       If given joint density and asked to ﬁnd conditional so need to ﬁnd marginals. Marginal is found from , and To convert from to polar, example: given ﬁnd , where , then write Use identity above.

law of total probablity: if we know and and want to know distribution of , then    where is of the sample.

Note Var(sample) has chi square (n) distribution.

CI for T: 