Search results with tag "Gambler s ruin problem"
1 Gambler’s Ruin Problem - Columbia University
www.columbia.edu1 Gambler’s Ruin Problem Consider a gambler who starts with an initial fortune of $1 and then on each successive gamble either wins $1 or loses $1 independent of the past with probabilities p and q = 1−p respectively. Let R n denote the total fortune after the nth gamble. The gambler’s objective is to reach a total
ONE-DIMENSIONAL RANDOM WALKS
galton.uchicago.eduSolve the gambler’s ruin problem for p q random walk by setting up and solving a difference equation. (Reformulate the difference equation as a matrix equation, and use this to represent the solution as a matrix multiplication. To get a simple formula …
1 Gambler’s Ruin Problem - Columbia
www.columbia.eduWhat is the probability that Ellen’s stock reaches the high value of $15 before the low value of $5? SOLUTION We want \the probability that the stock goes up by 5 before going down by 5." This is equivalent to starting the random walk at 0 with a= 5 and b= …