Download simple facts_Lecture 1 (Part II)

Simple Mathematical Facts for Lecture 1 (Part II)
Strong Law of Large Numbers
•
Let
X1, X2 ,...
be a sequence of independent random variables
having a common distribution, and
probability 1,
as
n ®+¥.
m = E [ Xi ].
X1 + X2 +... + Xn
®m
n
Then, with
Geometric Distribution
•
Suppose that independent trials, each having a probability
p of
being a success, are performed until a success occurs. If we let X be
the number of trials required until the first success, then
p. In particular,
n-1
P [ X = n] = (1- p) p
geometric distribution with parameter
for
n ³1.
X follows a