# Question 14938: The CDF Jump Is the Point Mass, Not the Whole CDF Value [Return to catalogue page 75](https://ocme.evemisslab.com/en/questions/page/75/) [← Question derivation index](https://ocme.evemisslab.com/en/questions/) · [Original question batch](https://ocme.evemisslab.com/en/practice/batch-20261014-advance-20261030-r06-cumulative-distribution-function-foundations/#q-20261014-advance-20261030-r06-cumulative-distribution-function-0038) This teaching derivation has second-context AI mathematical and bilingual semantic review, limited to the model and assumptions stated in this question. It has no human review or new Lean proof and does not promote the original question or MKO to Canonical truth. R0028-14938 · q-20261014-advance-20261030-r06-cumulative-distribution-function-0038 ## Original question and givens Use the complete finite discrete law with distinct integer support=[0, 7, 13] 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=0. Give (t,left_limit,F_t,point_mass,jump_identity?). - G001 — Use the complete finite discrete law with distinct integer support=[0, 7, 13] 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=0. Give (t,left_limit,F_t,point_mass,jump_identity?). ## 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](https://ocme.evemisslab.com/en/mko/mko-cumulative-distribution-function/) ## Step-by-step derivation S001 · calculationBefore CDF law total mass := sum(1/4, 1/4, 1/2) After CDF law total mass = 1 Conditions: none Compute exactly from original roles and established intermediates,retaining denominators,signs,indices and necessary guards. Step identifiers and dependenciesRule: exact_rational_arithmetic · Uses: G001 S002 · impliesBefore original ordered support=[0, 7, 13];raw aligned masses=[[1, 4], [1, 4], [1, 2]] After normalized aligned masses=[1/4, 1/4, 1/2];nonnegative=Yes;total=1 Conditions: none Qualify distinct support,nonnegative masses and unit total.Preserve original support-mass pairing even if unsorted,and retain zero-mass support points.This independently enforces the probability-law premise declared by the source English scope. Step identifiers and dependenciesRule: CDF_complete_probability_law_original_pairing · Uses: G001, S001 S003 · impliesBefore threshold CDF:original support index=0;value=0;threshold=0 After test value<=threshold=Yes;aligned mass=1/4 Conditions: none Test the threshold at each original support index and use its aligned mass.Distinguish strict< from inclusive≤;do not sort support while retaining old mass positions. Step identifiers and dependenciesRule: CDF_every_original_atom_threshold_guard · Uses: G001, S002 S004 · impliesBefore threshold CDF:original support index=1;value=7;threshold=0 After test value<=threshold=No;aligned mass=1/4 Conditions: none Test the threshold at each original support index and use its aligned mass.Distinguish strict< from inclusive≤;do not sort support while retaining old mass positions. Step identifiers and dependenciesRule: CDF_every_original_atom_threshold_guard · Uses: G001, S003 S005 · impliesBefore threshold CDF:original support index=2;value=13;threshold=0 After test value<=threshold=No;aligned mass=1/2 Conditions: none Test the threshold at each original support index and use its aligned mass.Distinguish strict< from inclusive≤;do not sort support while retaining old mass positions. Step identifiers and dependenciesRule: CDF_every_original_atom_threshold_guard · Uses: G001, S004 S006 · calculationBefore threshold CDF selected mass sum := sum(1/4) After threshold CDF selected mass sum = 1/4 Conditions: none Compute exactly from original roles and established intermediates,retaining denominators,signs,indices and necessary guards. Step identifiers and dependenciesRule: exact_rational_arithmetic · Uses: G001, S005 S007 · impliesBefore CDF left limit:original support index=0;value=0;threshold=0 After test value