The multiplication Principle
If one experiment has m outcomes and another experiment has n outcome,
then there are mn possible outcomes for the two experiments.
In general if there are p experiments and the rst one has 721 possible
outcomes; the second n2
October 5, 2016
1 Question 1
It was an hypergeometric distribution:
2 Question 2
Let p P pDies|normalq, then we know that:
P pDies highq P phighqP pDies|highq 0.8p
P pDiesq 0.5p ` 4 0.2p` 2 0.3p 1.9p
Midterm 1 solutions
October 12, 2016
1 Question 1:
Let pX1 , X2 q have the following p.d.f
@px1 , x2 q, f px1 , x2 q
, if px1 , x2 q P r0, 8q2
Let Y1 12 pX1 X2 q and Y2 X2 .
Find the pdf of pY1 , Y2 q.
Find the pdf of Y1
4.- Let X, Y be independent and have probability
( = ) = (2) , ( = ) = (2)
for , = 1,2,
Find the moment generating function of X+Y
Lets find the mgf of X
= ( ) =( ) = ( ) = [
If < 2
The Expectation Functions of Random
Why are we interested in this?
Let x be a r.v, and we have Y = g(x). Then Y is a r.v if
x and y are continuous.
y=g(x) so EY=Eg(x) is reasonable
it may be easie