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5 Howick Place | London | SW1P 1WGThe T Distribution also called the students t-distribution and is used while making assumptions about a mean when we don’t know the standard deviation. 19clarification neededbettersourceneeded
For
1
{\displaystyle \nu 1}
, the raw moments of the t-distribution are
Moments of order
{\displaystyle \nu }
or higher do not exist.
Equivalently, the random variable of the F-distribution may also be written
where
s
1
2
=
S
1
2
d
{\displaystyle s_{1}^{2}={\frac {S_{1}^{2}}{d_{1}}}}
and
s
2
2
=
S
check here
2
2
d
2
{\displaystyle s_{2}^{2}={\frac {S_{2}^{2}}{d_{2}}}}
,
S
1
2
{\displaystyle S_{1}^{2}}
is the sum of squares of
d
1
{\displaystyle d_{1}}
random variables from normal distribution
N
(
0
,
1
2
)
{\displaystyle N(0,\sigma _{1}^{2})}
and
S
2
2
{\displaystyle S_{2}^{2}}
is the sum of squares of
d
2
{\displaystyle d_{2}}
random variables from normal distribution
N
(
0
,
2
2
)
{\displaystyle N(0,\sigma _{2}^{2})}
. .