B********h
发帖数: 59 | 1 a dog 两维 random walk on an integer plane, 但是只有在 x=y or x=-y 时 才能见
到这只狗，what's the probability that you see the dog at (5,5)? |
c**********e
发帖数: 2007 | 2 It depends on starting point bah. |
B********h
发帖数: 59 | 3 y, forgot to mention it. starting at (0,0)
【在 c**********e 的大作中提到】
: It depends on starting point bah.
|
p*****k
发帖数: 318 | 4 for a fair simple 2D random walk, if one waits long enough,
isn't it prob of 1 event that the dog appears at any point?
(the conclusion also does not depend on the starting position,
only the dimension matters here)
am i missing anything obvious? |
Q***5
发帖数: 994 | 5 I guess he means:
what's the probability that the first time you see the dog, the dog is at (5
,5)
【在 p*****k 的大作中提到】
: for a fair simple 2D random walk, if one waits long enough,
: isn't it prob of 1 event that the dog appears at any point?
: (the conclusion also does not depend on the starting position,
: only the dimension matters here)
: am i missing anything obvious?
|
p*****k
发帖数: 318 | 6
ah i see. thanks. that makes sense and is a very interesting problem!
【在 Q***5 的大作中提到】
: I guess he means:
: what's the probability that the first time you see the dog, the dog is at (5
: ,5)
|
B********h
发帖数: 59 | 7 The answer is
P(0,0)=1-2/pi
p(n,n)=(2/pi)(1/(4n^2-1))
i don't remember the exact description of the problem, but i'll try to add
what i can remember later. |
w*****e
发帖数: 197 | 8 This sounds more like it. This kind of problem is really
unique. In general, it proceeds as following:
1. Write down the recursive equation for probabilities.
(everybody can do this part)
2. Guess solutions based on some reasonable boundary constraint.
(hard part, more of art than science in my mind).
3. The final distribution should be a linear combination of
solutions guessed in step 2. Normally it involves exp, sin
and cos or complex numbers.
4. Reduce the solution in 3 into an infinite sum a
【在 B********h 的大作中提到】
: The answer is
: P(0,0)=1-2/pi
: p(n,n)=(2/pi)(1/(4n^2-1))
: i don't remember the exact description of the problem, but i'll try to add
: what i can remember later.
|
p*****k
发帖数: 318 | 9 Blacksmith, for the answer you gave, i'm pretty sure the problem
does NOT have that x=-y absorbing boundary. it should be that
the dog could only be seen when its position satisfies x=y. |
B********h
发帖数: 59 | 10 y, u r right. i was confused. sorry.
【在 p*****k 的大作中提到】
: Blacksmith, for the answer you gave, i'm pretty sure the problem
: does NOT have that x=-y absorbing boundary. it should be that
: the dog could only be seen when its position satisfies x=y.
|
