h****0
发帖数: 485 | 1 假设一个simple random walk中, 每次向左和向右的概率是1/2, 如果定义T是第一次出
现连续两次向右的时间。那么T的expectation是多少？ | a**********n
发帖数: 59 | 2 is it like the process of tossing the coins, head/tail probability 0.5/0.5,
the expectation of T that two heads are tossed consecutively? then the
answer is 6 | H****E
发帖数: 254 | 3 it is the sum of prob that all previous direction is all HHHH.., or all
previous directions all HTHT... | J*X
发帖数: 302 | 4 Let's say we want two H's.
After the first two throws, we have four different results:
1. HH, we end the game with 2
2. HT, we have start over again
3. TT, we have start over again
4. TH, we have 1/2 chance to finish the game with one more throw. We also
have another 1/2 chance to have another throw and then start over again.
suppose E is the number of expected throws, then the above argument can be
summarized as,
E = 1/4*2 + 1/2*(2+E) + 1/4*(2+1+1/2*E)
solve it. |
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