Functions on two random variables
01
Review practice: 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
Sums of random variables
03
PDF of sum from joint PDF
Suppose the joint PDF of
and is given by: Find the PDF of
.
04
Poisson plus Bernoulli Suppose that:
and are independent Find a formula for the PMF of
. Apply your formula with
and to find .
05
Convolution for uniform distributions over intervals
Suppose that:
and are independent Find the PDF of
. (You may find it helpful to start by considering specific numbers for
.)
06
Sums of normals
- (a) Suppose
are independent variables. Find the values of and for which , or prove that none exist. - (b) Suppose
, in part (a). Find . - (c) Suppose
and . Find .