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Probability and inference
Random variables
IPS chapter 4.3
©
2006 W.H. Freeman and Company
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View Full Document Objectives (IPS chapters 4.3)
Random variables
Discrete random variables
Continuous random variables
Normal probability distributions
Random variables
A
random variable
is a variable whose value is a numerical outcome
of a random phenomenon.
A basketball player shoots three free throws. We define the random
variable
X
as the number of hits
A
discrete random variable
X
has a finite
number of possible values.
A basketball player shoots three free throws. The number of baskets
successfully made is a discrete random variable (
X
).
X
can only take the
values 0, 1, 2, or 3.
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View Full Document The
probability distribution
of a
discrete random variable
X
lists the
values and their probabilities:
The probabilities must add up to 1.
A basketball player shoots three free throws. The random variable
X
is the
number of hits. Assume that the probability of a hit or miss in any single throw
is 0.5, and that the throws are independent.
Value of
X
0
1
2
3
Probability
1/8
3/8
3/8
1/8
H

H
HMM
HHM
MHM
HMH
MMM
MMH
MHH
HHH
The probability of any event is the sum of the probabilities
p
i
of the
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This note was uploaded on 05/09/2009 for the course PAM 2100 taught by Professor Abdus,s. during the Spring '08 term at Cornell University (Engineering School).
 Spring '08
 ABDUS,S.

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