Probability geometric series summation

by aaaaaaaa   Last Updated October 10, 2019 05:20 AM

  1. Suppose 𝑋 ~ πΊπ‘’π‘œπ‘š(𝑝1) on {1, 2, 3, … }, π‘Œ ~ πΊπ‘’π‘œπ‘š(𝑝2) on {1, 2, 3, … }, and 𝑋 βŠ₯ π‘Œ. Let 𝑆 = 𝑋 + π‘Œ. Find 𝑃(𝑆 = 𝑠) under each condition.

a) Assume 𝑝 = 𝑝1 = 𝑝2.

b) Assume 𝑝1 β‰  𝑝2. After setting up your summation, identify π‘Ž, π‘Ÿ and 𝑛 in a finite geometric series using the below formula and evaluate your summation.

π‘Ž + π‘Žπ‘Ÿ + β‹― + π‘Žπ‘Ÿ^(π‘›βˆ’1) = π‘Ž(1 βˆ’ π‘Ÿ^𝑛) / 1 - r



Related Questions


Updated April 09, 2017 02:20 AM

Updated January 19, 2018 17:20 PM

Updated April 26, 2017 14:20 PM

Updated May 10, 2017 03:20 AM

Updated July 06, 2019 12:20 PM