See
http://en.wikipedia.org/wiki/Martingale_(probability_theory)#Examples_of_martingales
"Suppose each amoeba either splits into two amoebas, with probability p, or eventually dies, with probability 1 8722; p. Let Xn be the number of amoebas surviving in the nth generation (in particular Xn = 0 if the population has become extinct by that time). Let r be the probability of eventual extinction. (Finding r as function of p is an instructive exercise. Hint: The probability that the descendants of an amoeba eventually die out is equal to the probability that either of its immediate offspring dies out, given that the original amoeba has split.)"
http://en.wikipedia.org/wiki/Martingale_(probability_theory)#Examples_of_martingales
"Suppose each amoeba either splits into two amoebas, with probability p, or eventually dies, with probability 1 8722; p. Let Xn be the number of amoebas surviving in the nth generation (in particular Xn = 0 if the population has become extinct by that time). Let r be the probability of eventual extinction. (Finding r as function of p is an instructive exercise. Hint: The probability that the descendants of an amoeba eventually die out is equal to the probability that either of its immediate offspring dies out, given that the original amoeba has split.)"
選擇“Disable on www.wenxuecity.com”
選擇“don't run on pages on this domain”
