Tài liệu thống kê - LAMNGHIEPVN.INFO (Hưng Bùi) ď tài liệu, giáo án, bài giảng , luận văn, luận án, đồ án, bài tập lớn v...
Trang 1Examples of continuous probability
distributions:
The normal and standard normal
Sometimes data can be
modeled using certain
equations For example,
the normal distribution
Normal distribution
Trang 2The Normal Distribution
X
f(X)
Changing μ shifts the
distribution left or right
Changing σ increases or decreases the spread
The Normal Distribution:
as mathematical function (pdf)
2 ) (
2 1
2
1 )
x
e x
f
Trang 3The Normal PDF
1 2
2
1
dx e
x
It’s a probability function, so no matter what the values of
and , must integrate to 1!
Normal distribution is defined by its mean
and standard dev
E(X)= =
Var(X)= 2 =
dx e
x
x
2( )2 1
2
1
2 )
( 2
1 2
) 2
1 (
2
dx e
x
x
Trang 4**The beauty of the normal curve:
No matter what and are, the area between - and
+ is about 68%; the area between -2 and +2 is
about 95%; and the area between -3 and +3 is
about 99.7% Almost all values fall within 3 standard
deviations
68-95-99.7 Rule
68% of the data
Trang 5Example of normally distributed data
IQ scores are normal with a mean 100, standard deviation
of 15, so
What if we want to know the
probability of having an IQ below
110? (P(X<110) one of the first
things we should do in these types
of problems is draw a picture
Trang 6many standard deviations 110
is away from the mean
This is called the z-score
We have a table that gives us
probability of being less than a certain
z- score
So we look this number up in the table
So the probability of having an IQ below 110 is 0.7486
Trang 7Other distribution: (FYI)
The number of squared standard normal
added together is the degrees of freedom
This is used to test for independence
Trang 8Used in linear regression, and to test
where or not 3 or more groups can have
the same mean
It goes to a standard normal as
used in small samples