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Stat 400 Lecture 9
Spring 2012
Review (2.6)
•
Poisson Processes, Poisson distribution.
•
Mean, variance and m.g.f. of Poisson distribution.
•
Poisson Approximation to Binomial distribution.
Today’s Lecture (3.3)
•
Continuous random variable and its c.d.f.
•
Probability density function (p.d.f.), its properties.
•
Mean, variance, moment generating function
•
Percentiles for p.d.f.
•
Comparison between discrete and continuous random
variables
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Spring 2012
Continuous-type random variable and its c.d.f.
The random variable
X
is a continuous random variable
if
X
takes all values in an interval of numbers.
•
Wheel of fortune: the angle of the pointer is within
[0
o
,
360
o
)
.
•
The length of time it takes to check out at Walmart
in the weekend.
•
The time we wait to see the next volcano eruption in
the world.
Note:
•
When
X
is continuous,
P
(
X
=
x
) = 0
for all
x
.
The probability mass function is meaningless.
•
Although we cannot assign a probability to any value
of
X
, we are able to assign probabilities to intervals:
e.g.
P
(
X
= 1) = 0
, but
P
(0
.
999
≤
X
≤
1
.
001)
can be
>
0
.
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