event_independence

std.stats.event_independence · Level L0

The two sides of independence for events A and B on a finite probability space: P(A ∩ B) and P(A)·P(B), and their difference; A and B are independent when it is 0. When P(B) > 0 this is the same as P(A | B) = P(A); when P(B) = 0 the product form still applies and A and B are independent. Two events only: pairwise independence of three events does not give mutual independence.

P(A ∩ B) − P(A)P(B)

Signature

event_independence(p: f64[n], A: f64[n], B: f64[n]) → f64[], f64[], 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 the three masses, and the product of two in exact rational arithmetic, on all 40 test cases.
All 120 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

dot

Called by

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sha256:106d2988a70c5b208144df595735c22c6d69bbb9487291686665cc697ac18169

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.event_independence · Ω:event_independence
Pins: sha256:f78868f4d9bfb35232d0ca6be627d666e203bf62590b0fb786c87eea76ecb73cthis graph and the 1 it reaches through calls
Evidence: sha256:9cc8fb7926a3e709c5c36e90d651540fab95b658ca769cee84e415ee4383f108the 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.