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:
The geometric distribution is the only discrete memoryless random distribution. It is a discrete analog of the exponential distribution. continuous
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: