1
Today
….
•
Expected Value (“mean”) of
h(X) :
•
Variance of X :
Recap …
(Probability) Distribution of
X
means the specification of:
•
P
robability
M
ass
F
unction (pmf of X) :
•
C
umulative
D
istribution
F
unction
(cdf of X):
p
X
(x) = P( X = x) = P ( { s
ε
S
: X(s) = x } )
F
X
(x) = P( X ≤ x) = P ( { s
ε
S
: X(s) ≤ x } )
Some numerical
summary measures
of the distribution of
X:
Section 3.3
Expected Value of Discrete RV
X
Uses:
1.
Provides a numerical summary of a distribution
2.
Typical value of
X
if the experiment is repeated many times
Example: Pay $50 to play the following game:
Spin,
X
= outcome
Section 3.3

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