Question 14982: A Finite-Law CDF Stays Constant Just to the Right

Original question and givens

Use the complete finite discrete law with distinct integer support=[-6, 1, 7] and aligned nonnegative exact masses=[1/4, 1/4, 1/2], summing exactly to 1. Preserve support-to-mass alignment even when support is not sorted. F(t)=P(X≤t) includes equality. The CDF is not a point mass or density: its jump at t is P(X=t), it is nondecreasing and right-continuous, with endpoint limits 0 and 1. Keep exact reduced rational outputs with positive denominators, omitting /1 for integers. Threshold t=-6. Give (t,F_t,next_support,constant_on_right_neighborhood_before_next_support,right_continuous?). next_support is the least support value strictly above t, or null when none exists.

• G001 — Use the complete finite discrete law with distinct integer support=[-6, 1, 7] and aligned nonnegative exact masses=[1/4, 1/4, 1/2], summing exactly to 1. Preserve support-to-mass alignment even when support is not sorted. F(t)=P(X≤t) includes equality. The CDF is not a point mass or density: its jump at t is P(X=t), it is nondecreasing and right-continuous, with endpoint limits 0 and 1. Keep exact reduced rational outputs with positive denominators, omitting /1 for integers. Threshold t=-6. Give (t,F_t,next_support,constant_on_right_neighborhood_before_next_support,right_continuous?). next_support is the least support value strictly above t, or null when none exists.

Definition and scope

Use the original question domain, assumptions and cited MKO definitions. This item has second-context mathematical and bilingual review, with the model, answer and every arithmetic step independently recomputed from the original parameters; the source question remains a candidate.

• mko-cumulative-distribution-function

Step-by-step derivation

CDF law total mass := sum(1/4, 1/4, 1/2)

CDF law total mass = 1

original ordered support=[-6, 1, 7];raw aligned masses=[[1, 4], [1, 4], [1, 2]]

normalized aligned masses=[1/4, 1/4, 1/2];nonnegative=Yes;total=1

threshold CDF:original support index=0;value=-6;threshold=-6

test value<=threshold=Yes;aligned mass=1/4

threshold CDF:original support index=1;value=1;threshold=-6

test value<=threshold=No;aligned mass=1/4

threshold CDF:original support index=2;value=7;threshold=-6

test value<=threshold=No;aligned mass=1/2

threshold CDF selected mass sum := sum(1/4)

threshold CDF selected mass sum = 1/4

CDF next support gap := sub(1, -6)

CDF next support gap = 7

CDF right neighborhood radius := div(7, 2)

CDF right neighborhood radius = 7/2

threshold=-6;F_t=1/4;next declared support=1;delta=7/2>0

for every0<=h<delta,no support lies in(t,t+h];F(t+h)=1/4=F(t)

Reverse checks

• S009 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence.
• S008 · premise_and_result_audit — Recompute CDF right neighborhood radius with exact rational arithmetic, not rounded decimals.
• S007 · premise_and_result_audit — Recompute CDF next support gap with exact rational arithmetic, not rounded decimals.
• S006 · premise_and_result_audit — Recompute threshold CDF selected mass sum with exact rational arithmetic, not rounded decimals.
• S005 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence.
• S004 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence.
• S003 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence.
• S002 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence.
• S001 · premise_and_result_audit — Recompute CDF law total mass with exact rational arithmetic, not rounded decimals.

Result

(-6, 1/4, 1, constant_on_right_neighborhood_before_next_support, Yes)

The full substitutions and premise checks give the original answer; source identity,format and status are unchanged.

This question review and source binding

Review date: 2026-10-26

Original questions, answers, step expressions, numeric ASTs and historical records are retained. Source candidate labels remain historical and are not overwritten as formal proof.