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AMS 572 Lecture Notes #1
Sep. 3
rd
, 2010
Review Probability:
Eg. 1.
Suppose each child’s birth will result in either a boy or a girl with equal probability.
For a randomly selected family with 2 children, what is the chance that the chosen family has
1) 2 boys? 2) 2 girls? 3) a boy and a girl?
Solution: 25%; 25%; 50%
P(B and B)= P(B∩B)= P(B)∙P(B)=0.5∙0.5=0.25
P(G and G)= P(G∩G)= P(G)∙P(G)=0.5∙0.5=0.25
P(B and G)= or =
Binomial Experiment:
1)
It consists of n trials
2)
Each trial results in 1 of 2 possible outcomes, “S” or “F”
3)
The probability of getting a certain outcome, say “S”, remains the same, from trial to
trial, say P(“S”)=p
4)
These trials are independent, that is the outcomes from the previous trials will not
affect the outcomes of the upcoming trials
Eg. 1
(continued)
n=2, let “S”=B, P(B)=0.5
Let X denotes the total # of “S” among the n trials then
X~B(n, p)
Its probability density function (pdf) is
,
x=0,1,…,n
**For a discrete random variable, its pdf is also called its probability mass function (pmf)
1
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 Fall '10
 WeiZhu

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