rv_independence

std.stats.rv_independence · Level L1

Independence of two finite random variables from their joint table J (J[x, y] = P(X = x, Y = y)): the marginals of X and Y, the deviation J − P(X)·P(Y)ᵀ, and its largest magnitude. X and Y are independent exactly when every entry of the deviation is 0. Zero covariance is a consequence of independence, not a test for it.

J − p_X p_Yᵀ

Signature

rv_independence(J: f64[a, b]) → f64[a], f64[b], f64[a, b], f64[]

Structure

The function as NOVA stores it: one box per input, operation and output, and arrows that carry values. A double border marks another library function this one runs — called once, or by Scan once per element; select it to open that function.

input
operation
constant
call
output

Verification

Signature proven by NOVA’s shape solver, for every size.
Equal to the reference row and column sums, the outer product, the largest gap in exact rational arithmetic, on all 40 test cases.
All 1,124 float64 results are exact: the error is zero.
Interpreter and NumPy backend return bit-identical results.
At float32 too: the 40 test cases rounded to float32, and 40 of them exact, with zero error.

Accuracy in detail

correctly rounded (the float64 nearest the exact value): 100%
bit-equal to the NumPy formula in float64: 100%
largest error, in units in the last place: 0

Identity

Calls

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Called by

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sha256:423f0b07147834b2f6bb1972fea2777b2cca75697e0f595d6583e98873d5f2f6

The semantic hash of the graph. It changes when the program changes, and never when only its documentation does.

Control handle

Symbol: Ω:std.stats.rv_independence · Ω:rv_independence
Pins: sha256:5241fc3e98c9b101000a50dab27aa782b2a364fb52288c89f8b554f1d810f0f7this graph alone
Evidence: sha256:b2dd8c61cb14997fabed0101985c2eaad40d231dccd54e3baedbdc18d10e6b45the hash of its verification record
Needs: no capability: a pure function

Through NOVA’s control layer, the symbol launches this function only while the program still matches what it pins: a change to this graph, or to any graph it reaches, needs a migration first.