Statistics 400
Lecture 13 (Sep 23)
Continuous Distributions
Random Variable:
(R.V.) is a variable whose value is a numerical outcome
of a random phenomenon.
Notation
: X, Y, Z
Note
: When a random variable X describes a random phenomenon, the
sample space S just lists the possible values the random variable takes.
Discrete Random Variables:
•
A discrete R.V. has a countable number of possible outcomes
•
These outcomes have a individual probabilities attached to them
Probability Distributions:
•
Lists the values of X
•
Lists their respective probabilities
Value of X
x
1
x
2
x
3
x
4
x
5
…
…
x
k
Probability
mass
function :
f(x)
f(x
1
)
f(x
2
)
f(x
3
)
f(x
4
)
f(x
5
)
…
…
f(x
k
)
Properties of p.m.f
f(x)
: (a)
f(x)>0;
(
b
)
∑
=
1
)
(
x
f
;
(
c
) P(X=x)=f(x).
Ping Ma
Lecture 13
Fall 2005
 1 
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View Full DocumentContinuous Random Variables:
•
Takes on all values in an interval of numbers
•
The probability distribution of X is described by a probability density
function (p.d.f).
•
The probability of an event is the area under the p.d.f. and over the
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 Fall '05
 TBA
 Statistics, Probability theory, probability density function, µ, Ma Lecture

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