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| Name | Range | Parameters | p.d.f | c.d.f. | Expectation | Variance |
| Normal N ( &mu. , &sigma.&powtwo. ) |
~y &in. &reals. | &mu. &in. &reals. &sigma.&powtwo. &in. &reals.^+ |
fract{1,&sqrt.${2&pi.&sigma.&powtwo.}} exp rndb{fract{- (~y - &mu.)^2,2&sigma.&powtwo. }} | _ | &mu. | &sigma.&powtwo. |
| Student's t t ( ~k ) |
~y &in. &reals. | ~k &in. &naturals.^+ | fract{&Gamma.( (~k+1)/2 ) (1 + ~y^2/~k)^{-(~k+1)/2},&Gamma.( ~k/2 ) &sqrt.${~k&pi.}} | _ | _ | _ |
| Chi-squared &chi.^2 ( ~k ) |
~y &in. &reals. ~y > 0 |
~k &in. &naturals.^+ | fract{~y ^{~k/2 - 1} e ^{-~y/2} , 2 ^{~k/2} &Gamma.( ~k/2 )} | _ | ~k | 2~k |
| Gamma &Gamma. (&alpha. , &beta. ) |
~y &in. &reals. ~y > 0 |
&alpha. &in. &reals.^+ &beta. &in. &reals.^+ |
fract{&beta.^{&alpha.} ~y^{&alpha. - 1} e^{-&beta.~y} , &Gamma.( &alpha. )} | _ | &alpha. ./ &beta. | &alpha. ./ &beta.^2 |
| F F ( ~d_1 , ~d_2 ) |
~y &in. &reals. ~y > 0 |
~d_1 &in. &naturals.^+ ~d_2 &in. &naturals.^+ |
fract{(&nu._1 ./ &nu._2) &Gamma.( (&nu._1 + &nu._2) ./ 2 ) (&nu._1 ~y ./ &nu._2)^{(&nu._1 ./ 2) - 1} , &Gamma.( &nu._1 ./ 2 ) &Gamma.( &nu._2 ./ 2 ) ( 1 + (&nu._1 ~y ./ &nu._2) )^{(&nu._1 + &nu._2) ./ 2} } | _ | _ | _ |
| Exponential M( &beta. ) |
~y &in. &reals. ~y > 0 |
&beta. &in. &reals.^+ |
&beta. e^{- &beta.~y} |
1 - e^{- &beta.~y} | 1 ./ &beta. | 1 ./ &beta.&powtwo. |
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