## Distributions Summary

Click on the distribution name to go to the look-up facility.

 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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