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# 10C. Math & Stats

`m0=: median=: <.@-:@# { /:~` | Median of y
`m1=: tc=: (+. +./ .*.~)^:_` | Transitive closure of connection matrix y
`c2=: ^:` | Apply function x y times
`c3=: ^:` | Conditional application of x if y is 0 or 1
`m4=: gamma=: !@<:` | Gamma function of y
`d5=: beta=: *&m4 % m4@+` | Beta function of x and y
`d6=: pd=: ^@-@] * ^~ % !@[` | Poisson distribution of states x with average number y
`d7=: outof=: !` | # of combs of y objects taken x at a time
`d8=: ppr=: +//.@(*/)` | Product of polynomials x and y
`m9=: -<./"1` | Move rows of table y into first quadrant
`m10=: npb=: p:^:_1` | Number of primes before y
`m11=: pto=: p:@i.@npb` | List of primes to y
`d12=: dpr=: [: 0 2 1 3&|: */` | Direct matrix product of x and y
`d13=: shurp=: (0 2;3 1)&|:@(*/)` | Shur product of x and y
`d14=: shurs=: (0 2;3 1)&|:@(+/)` | Shur sum of x and y
`m15=: <./ .+~` | Extend distance table to next leg
`d16=: +./ .*.` | Extend a transitive binary relation
`d17=: +/ .* % #@]` | Mean of x weighted by y
`d18=: -/ .%` | Alternating sum of reciprocal series x%y
`d19=: +/ .%` | Sum of reciprocal series x%y
`d20=: +/ .*` | Matrix product
`d21=: +/ .*` | Sum over subsets of x located by y
`m22=: +/ .*~` | Sum of squares of y
`d23=: +/ .*` | Scalar (dot) product of vectors x and y
`d24=: */ .^` | Product over subsets of x located by y
`m25=: +/@:*:` | Sum of squares of y
`m26=: det=: -/ .*` | Determinant
`m27=: (+/@(*:@(] - +/ % #)) % #}"1` | Sample variance (dispersion) of y
`m28=: %:@m27"1` | Standard deviation of y
`d29=: (+/@((]-+/@]%#@])^[)%#@])"1` | xth moment of y
`m30=: m31"1` | Mean of rows of table y
`m31=: +/%#` | Mean of list y or columns of table y

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