Several Probabilistic Problems for Runs

• Main Authors: Kuan-Chou Chen, 陳冠洲
• Other Authors: Dr. Shoou-Ren Hsiau
• Format: Others
• Language: en_US
• Published: 2010
• Online Access: http://ndltd.ncl.edu.tw/handle/63182777825493761499

碩士 === 國立彰化師範大學 === 數學系所 === 98 === In this thesis we study the run-related problems. The distribution and expectation of the waiting time for the kth run are given for i.i.d Bernoulli trials. Moreover, we derive the expectation of the waiting time for three-state trials. We are also interested in the lengths of runs in Bernoulli trials. The waiting number of runs for the first occurrence that the lengths of runs increase (or decrease) is discussed. We derive its distribution and an upper bound for its expectation. At the end, we derive the distribution of the number of runs on a circle for arranging a 1's and b 0's and then for the i.i.d Bernoulli trials.