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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.
- 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: