STATISTICS
WEEK 9 : CONTINUOUS DISTRIBUTION AND SAMPLING DISTRIBUTION
# F Distribution
.
# Sampling Distribution
# Distribution
2
Edensity function is given by :
=
F
+ It)
G
-cat
#70
- 4)
.
a V, is the "numerator" degrees of freedom
b V2 is the "denominator" degrees
of freedom
b>
4
2) The mean and variance
of an F random variable are given by :
meani
ECF) V ELF V272
= V2-2
2Vz (Vi + Vz-2)
and
,
N(F)
=
-
CVV VCV2-2)2(ve-yi
v(F) = va > Y
↑ distribution is similar to the X- distribution
that its starts at zero (is non-negative) and I not symmetrical .
-
Determining Values of
F
example : what is the value of O
F for
G
% 5
of the area
under
with
me
a numerator
right hand" tail" of the
degree
freedom of
-
of
curve
,
3 VI Fo .5 , 3 7 ,
-
of 7 ? V2
and
- dominator degree
of freedom
answer : There are
different tables
for different values
of .
A
Make sure
you start with the correct table
.
· F . 0, 5 , 3, 7
critical values of F, A = . 0 ,5
numerator COLUMN
degrees of freedom
:
Row
denominator degrees of freedom
:
, For areas under the
-
curve on the
left hand side of the curve
,
numerator denominat
we can
leverage the following relation shin
right = FA VI , V2
,
left=
-
F1-A
ve
V 12 =
, ,
Fa , ,
vi
Ea ,
Vz , VI
(the order
change
Sampling Distribution
A distribution is created by sampling
sampling .
The method
of probability and
we will employ on the rules
the laws expected value and to derive the distributionn.
of variance
sampling
M SAMPLING DISTRIBUTION OF THE MEAN
A
fair die is thrown infinitely many times
,
with the random variable X =
*
of spots of any throw
-
The mean = m = PCC)
Variance >
- " =
z(x -
4) P(x)
5 =
w
·
of
Compare
compare the distribution X , with the
sampling distribution of
.
X
of
A well, , note that :
Mx = M
o = 02/2
x
·7 Generalize
Generalize the mean and variance of the sampling of two dice :
Mic = Y
of = 02/2
--- to n-dice =
Mic = M The standard deviation of
5,3 52 E
the sampling distribution 5
= =
n
is called the standard error : F
WEEK 9 : CONTINUOUS DISTRIBUTION AND SAMPLING DISTRIBUTION
# F Distribution
.
# Sampling Distribution
# Distribution
2
Edensity function is given by :
=
F
+ It)
G
-cat
#70
- 4)
.
a V, is the "numerator" degrees of freedom
b V2 is the "denominator" degrees
of freedom
b>
4
2) The mean and variance
of an F random variable are given by :
meani
ECF) V ELF V272
= V2-2
2Vz (Vi + Vz-2)
and
,
N(F)
=
-
CVV VCV2-2)2(ve-yi
v(F) = va > Y
↑ distribution is similar to the X- distribution
that its starts at zero (is non-negative) and I not symmetrical .
-
Determining Values of
F
example : what is the value of O
F for
G
% 5
of the area
under
with
me
a numerator
right hand" tail" of the
degree
freedom of
-
of
curve
,
3 VI Fo .5 , 3 7 ,
-
of 7 ? V2
and
- dominator degree
of freedom
answer : There are
different tables
for different values
of .
A
Make sure
you start with the correct table
.
· F . 0, 5 , 3, 7
critical values of F, A = . 0 ,5
numerator COLUMN
degrees of freedom
:
Row
denominator degrees of freedom
:
, For areas under the
-
curve on the
left hand side of the curve
,
numerator denominat
we can
leverage the following relation shin
right = FA VI , V2
,
left=
-
F1-A
ve
V 12 =
, ,
Fa , ,
vi
Ea ,
Vz , VI
(the order
change
Sampling Distribution
A distribution is created by sampling
sampling .
The method
of probability and
we will employ on the rules
the laws expected value and to derive the distributionn.
of variance
sampling
M SAMPLING DISTRIBUTION OF THE MEAN
A
fair die is thrown infinitely many times
,
with the random variable X =
*
of spots of any throw
-
The mean = m = PCC)
Variance >
- " =
z(x -
4) P(x)
5 =
w
·
of
Compare
compare the distribution X , with the
sampling distribution of
.
X
of
A well, , note that :
Mx = M
o = 02/2
x
·7 Generalize
Generalize the mean and variance of the sampling of two dice :
Mic = Y
of = 02/2
--- to n-dice =
Mic = M The standard deviation of
5,3 52 E
the sampling distribution 5
= =
n
is called the standard error : F
