Crime in Boston

El presente estudio analiza la aplicación de métodos de simulación Monte Carlo en el modelado de variables aleatorias continuas y discretas mediante el lenguaje de programación R. A partir de distribuciones Gamma y Bernoulli, se evalúa la convergencia de medias y proporciones para diferentes tamaños muestrales. Asimismo, se examinan los fundamentos de la Ley de los Grandes Números y el Teorema del Límite Central, utilizando datos sintéticos en un contexto académico.

US Diesel Sales Price (GASDESW) Latest reading (week of Oct 5, 2026): $6.199. Record high: $6.529 (week of Sep 21, 2026). Key periods and drivers 2020 – Pandemic collapse Prices started the year near $3 and fell sharply with the COVID-19 demand shock (freight, travel, and economic activity plunged). They bottomed near $2.37 in late 2020. Annual average was the lowest of the period at $2.55. ### 2021 – Recovery and rising demand Prices climbed steadily as the economy reopened and goods demand recovered. Average rose to $3.29, still well below later peaks. 2022 – Sharp spike to then-record highs Russia’s full-scale invasion of Ukraine in February triggered a major supply shock. Russia is a large exporter of diesel/gasoil; sanctions, trade disruptions, and low global distillate inventories drove prices sharply higher. The weekly high reached $5.810 in June 2022; the annual average hit $4.989 (previous record until 2026). Diesel’s premium over gasoline also widened significantly. 2023–2025 – Gradual decline and stabilization Prices eased from the 2022 peak as markets adjusted, inventories improved somewhat, and crude oil moderated. Annual averages fell to $4.21 (2023), $3.76 (2024), and $3.66 (2025). Prices mostly traded in a relatively narrow $3.45–$4.10 range for much of 2024–2025. 2026 – New record surge Prices started the year near the recent lows (~$3.46 in mid-January) but rose dramatically from March onward. By September they set successive new highs, peaking at $6.529 before easing slightly to $6.199 by early October. Year-to-date average is already $5.04—higher than any prior full-year average. Primary drivers of the 2026 spike (a refining/product shortage more than a pure crude shortage): Prolonged disruption/closure effects in the Strait of Hormuz linked to Middle East conflict (U.S./Israel–Iran tensions beginning around late February). Russian diesel export restrictions/bans (and reduced output from Ukrainian strikes on Russian refineries). Very tight global distillate inventories, high U.S. refinery utilization (near 98% at times), and competition from high-margin jet fuel production. Resulting elevated diesel crack spreads (refining margins). Overall pattern From the 2020 trough near $2.40 to the 2026 peak above $6.50, the series more than doubled at the extremes. The 2022 and especially 2026 episodes show how diesel—critical for trucking, agriculture, rail, and freight—is more sensitive than gasoline to refined-product supply shocks and geopolitical disruptions affecting Russia and the Middle East. Prices remain elevated relative to the 2020–2021 and 2024–2025 ranges as of early October 2026.