01
Function on one variable
Suppose the PDF of
is given by: Find the CDF and PDF of
.
02
PDF of Min and Max
Suppose
and and these variables are independent. Find: (a) The PDF of
(b) The PDF of
03
PDF of a Min
Let
and be independent copies of a random variable. Let
. Find the PDF of .
04
Coffee and danish
Joe visits a coffee shop every morning and orders a triple espresso and a cherry danish. Let
represent the wait time for the espresso and the wait time for the danish (both in minutes). The joint PDF of and is: Suppose that Joe will not sit down until he has both his espresso and his danish. Compute the probability that he will have to wait at least 5 minutes before sitting down, that is, find
.