D**u
发帖数: 204 | 1 A guy starts walking from position x_0 on earth (we treat earth as a sphere
with radius R). He randomly chooses a direction and walk 1 meter (this is
the spherical distance) and reaches position x_1. He repeats the walk n
times and arrives at position x_n.
Question:
(1) what is E((x_n - x_0)^2)? (here ((x_n - x_0)^2 is the square of the
Euclidean distance, not the spherical distance).
(2) does E((x_n - x_0)^2) converge when n --> \infty? |
|
t**o
发帖数: 64 | 2 比如
aX+bY， a&b are arbitrary r.v. ，X&Y are independent Gaussian. If a&b are
independent of X&Y, is the random combination still Gaussian?
heuristic explanation?
thx! |
|
j****x
发帖数: 943 | 3 正在看一哥们写的turbulence，他说randomness 就一定是stochastic，但
deterministic的
方程也能出一stochastic的解,靠谱吗？ |
|
o*******w
发帖数: 349 | 4 "Correction to 'entropy and maximal spacings for random partitions'"
by Eric Slud
Probability Theory and Related Fields, Volume 60, Number 1 (1982)
请发至
M*************[email protected] |
|
x*****i
发帖数: 287 | 5 【 以下文字转载自 ME 讨论区 】
发信人: xiguapi (guagua), 信区: ME
标 题: 请教：用Ansys模拟random media的有效permittivity
发信站: BBS 未名空间站 (Wed May 28 11:09:56 2014, 美东)
我用matlab做了一个三维空间矩阵50x50x50，里面随机分布着水、泥土还有黄铜三种物
质颗粒,一个网格就代表一个种物质。
我能把这个geometry导入到Ansys里面算高频的effective permittivity吗？
有没有关于这方面的instruct或者manual？
谢谢。 |
|
w*******a
发帖数: 2409 | 6 那位能提供点关于random-and-for-cause drug testing的介绍或者网页么？多谢 |
|
w*******a
发帖数: 2409 | 7 那位能提供点关于random-and-for-cause drug testing的介绍或者网页么？多谢 |
|
|
N***c
发帖数: 1090 | 9 最近在研究一个课题，是关于如何使不规则形状的物体更密实的堆垛的问题。这些物体
大多是立方的，片状的，也有可能是球形的，无法选择。这个题目也可以变化成什么样
的容器可以使这些物体堆得更密。
网上找了一圈没看到什么太相关的文献。感觉应该跟random close pack有关。大家觉
得这个题目跟哪个领域比较接近呢？ |
|
y**c
发帖数: 133 | 10 Sorry, I did not explain it clearly.
There are some gas in a sphere. For one particle, it is randomly walking,
Brown motation, and at the same time, this particle can see the potential
which is exponentially dropping depend on how close to the wall of the
sphere, exp(-(R0-R)/a).
The potential itself is static, i.e. is NOT of function of t. But the
potential seen by the particles are not static. It is a function of space,
and time. In this question, Fourier transfer of auto-correlation function |
|
x*****i
发帖数: 287 | 11 【 以下文字转载自 EE 讨论区 】
发信人: xiguapi (guagua), 信区: EE
标 题: 请教：用Ansys模拟random media的有效permittivity
发信站: BBS 未名空间站 (Wed May 28 11:07:08 2014, 美东)
我用matlab做了一个三维空间矩阵50x50x50，里面随机分布着水、泥土还有黄铜三种物
质颗粒,一个网格就代表一个种物质。
我能把这个geometry导入到Ansys里面算高频的effective permittivity吗？
有没有关于这方面的instruct或者manual？
谢谢。 |
|
B*********h
发帖数: 800 | 12 ☆─────────────────────────────────────☆
jjwwjj (jjwwjj) 于 (Sun Nov 12 14:38:49 2006) 提到:
X1, X2,...,Xn are independent random variables, uniformly distributed on [0,
1]. What is the probability that X1+X2+...Xn<1.
☆─────────────────────────────────────☆
matII (当归) 于 (Sun Nov 12 14:50:59 2006) 提到:
直接积分就得了。
0,
☆─────────────────────────────────────☆
zdg (zdg) 于 (Sun Nov 12 15:08:01 2006) 提到:
I think it is 1/(n!)
0,
☆─────────────────────────────────────☆
jjwwjj (jjwwjj) 于 (Sun |
|
B*********h
发帖数: 800 | 13 ☆─────────────────────────────────────☆
loveleader (hatefree) 于 (Tue Feb 20 23:39:30 2007) 提到:
对于asymmetric random walk, 该怎么处理
reflection principle?
我得想法是 # above / # total = p
# below / # total = q
P(# above)/p = P(# below after reflected)/q
不知道这么想对不对.
请帮忙指点一下.
谢谢!
☆─────────────────────────────────────☆
zdg (zdg) 于 (Wed Feb 21 08:13:02 2007) 提到:
read this
http://www.mitbbs.com/mitbbs_article_t.php?board=Quant&gid=16877965&ftype=0 |
|
A*S
发帖数: 24 | 14 A simple random walk St with S0 = 0 and p < 1. How to show that
M = max(St : t>=0) satisfies
P(M>=x)=(p/q)^x.
Thanks. |
|
f****e
发帖数: 590 | 15 a sequence of iid random variable |
|
f*********1
发帖数: 117 | 16 谢谢findle!
你的意思是the average of a sequence of iid RVs?
a sequence of iid random variable |
|
n******r
发帖数: 1247 | 17 this is not right
a sequence of iid random variables converges with probability 1
an example for 1 doesn't imply 2 can be
toss a fair coin
X=1 if head, 0 if tail
Y=1 if tail, 0 if head
X Y have the same cumulative distribution, but for e<1,P(|X(w)-Y(w)|>e)=1
therefore no convergence in probability |
|
c******e
发帖数: 101 | 18 If X, Y, and Z are 3 random variables such that X and Y are 90% correlated,
Y and Z are 80% correlated, what is the minimum and maximum correlation that
X and Z can have?
Dam hard |
|
m******e
发帖数: 45 | 19 How to generate uniform [0,1] distributed random numbers with correlation
rho?
generating correlated gaussian r.vs are trivial, but it seems there is no
clean way
for uniform r.v. , any idea? thanks. |
|
b***k
发帖数: 2673 | 20 ☆─────────────────────────────────────☆
forrestarrow (linzhongxianjian+) 于 (Tue Oct 16 10:47:42 2007) 提到:
这个问题好像在本版出现过，一直没有想清楚，请教大家
1D random walk, 问到达 -5 之前到达2的概率？谢谢
☆─────────────────────────────────────☆
EM (EM Algorithm) 于 (Tue Oct 16 11:28:11 2007) 提到:
5/7
☆─────────────────────────────────────☆
forrestarrow (linzhongxianjian+) 于 (Tue Oct 16 11:45:15 2007) 提到:
能讲一下解的思路马？谢谢
☆─────────────────────────────────────☆
xchric (FX) 于 (Tue Oct 16 16:13:03 2007) 提到:
如果是symmetric |
|
o***a
发帖数: 724 | 21 【 以下文字转载自 Mathematics 讨论区 】
发信人: olama (Obama), 信区: Mathematics
标 题: 有啥好的normal distribution random variable的C代码？
发信站: BBS 未名空间站 (Sun May 17 02:19:12 2009), 站内
大家能推荐一个好的么
3x |
|
p******i
发帖数: 1358 | 22 nice solution,thx
where xn is the dollar amount you win after n rounds, and apply optimal
stopping theorem. in general the martingale is [p(H)/p(T)]^(-xn). the
desired prob satisfies the eq.:
probability of winning at least $a before losing $b (note the forward jump
is 2 - the random walk could pass "a" without hitting it). the optimal
stopping theorem does not work too well here, as one could stop at either a
or a+1. instead denote p(n) as the desired prob if one starts with $n. the
recur |
|
p*****k
发帖数: 318 | 23 i recall that unless the step size of the random walk shrinks to zero, i.e., a Brownian motion, it does not have a limiting distribution (for BM, it's simply diffusion on a closed surface, thus uniform). so i would naively think the answer to (2) is no. i will try (1) when i get more time. |
|
r******r
发帖数: 138 | 24 just an intuitive solution:
transform the spherical distances to radians, do 2-d random walk on a plane, then take the remainder of |An-A1|/(2pi) where Ai = (alpha_x,alpha_y) radian, and calculate the corresponding
euclidian distance.
as n goes to infinity, the expectation doesn't converge b/c of this "
periodicity" of 2pi.
sphere |
|
y*a
发帖数: 7 | 25 It actually has a very elegant ansewer:
E[ |x_n-x_0|^2] = 2*R^2 - 2*R^2*cos(theta)^n
where theta = a/R, a is the distance walked each time (in this case, a=1
meter)
and it converges to 2*R^2 when n --> infinity.
Also if let R --> infinity, the result approaches n*a^2, whihc is the result
for a 2-D random walk on a flat plan.
Simple vector analysis can get you the answer. |
|
D**u
发帖数: 204 | 26 Thanks, I will try to read it.
A few more words about the problem.
If we substitute the "spherical random walk"
with "spherical brownian motion", and replace x_n with x_t (t is the time),
then
E((x_t - x_0)^2) = 2 - 2*exp(-t/2).
When t --> 0, the above value is close to t, which coincides with the planar
case. |
|
y*a
发帖数: 7 | 27
Sure. Here is my derivation:
if x_i is the location vector originated from the center of the sphere, then
we have
x_i = R * p_i, where p_i is the unit vector in the same direction as x_i
then
R*p_i+1 = R*cos(theta)*p_i + R*sin(theta)*t_i --- (1)
where t_i is an random unit vector with a uniform distribution
in all directions that are perpendicular to p_i. and
theta = a/R, where a is the distance walked each time ( in this question, a
= 1 meter).
from (1) we have
p_n = p_0 * (cos(theta))^n +
|
|
y**k
发帖数: 222 | 28 求一维对称 Random walk 最终回到出发点的概率.
据一个朋友说， 他面试的人能清楚解释这个的很少， 他们都要了。 一些哈佛，
MIT 的面试者都不能。 |
|
t**o
发帖数: 64 | 29 比如
aX+bY， a&b are arbitrary r.v. ，X&Y are independent Gaussian. If a&b are
independent of X&Y, is the random combination still Gaussian?
heuristic explanation?
thx! |
|
b***k
发帖数: 2673 | 30 it's a standard symetric random walk problem, typically 3 ways to solve it,
level is counted as easy approach to hard one
1. apply martingale stopping theorem
2. Markov chain approach
3. conditional probability method
before |
|
s********t
发帖数: 31 | 31 This is not the Gambler's ruin problem although relevant.
An object does random walk on a number line.
At time zero it is at location zero.
Probability to move to left (negative direction) is p. Here p>1/2
Probability to move to right (positive direction) is q=1-p.
Questions:
a. What is the expected number of steps for the object to get to -10?
b. What is the expected number of steps for the object to get to 10?
My thought for a is: Expected change per step (conditioned on the directino
of |
|
D**u
发帖数: 204 | 32 Heard the following interesting question.
Let x be a random variable, and y = min(x,1).
Prove that var(x) >= var(y). |
|
B****n
发帖数: 11290 | 33 Let f(x) denote the density (or probability) of X.
The distribution of min(X,1) is the same as the distribution of the sum
P(X<=1)*G+P(X>1)*1, where the random variable G has conditional density f(x|
X<=1).
So the variance of X is equal to P(X<=1)^2*Var(G).
Var(X)>=E(Var(X|I{X<=1}))>=P(X<=1)*Var(X|X<=1), where I is an indicator
function.
So Var(X)>=P(X<=1)^2*Var(X|X<=1)=Var(min(X,1)) |
|
s******a
发帖数: 184 | 34 用accept/rejection method 产生 random sample，
发现对有些分布拟合得很好，对有些就不好，这有规律可循吗？ |
|
s*******i
发帖数: 546 | 35 一个random walk start from 0. each step size has the probability of:
-1 (0.2), 0(0.2) and 1 (0.6). Find the probability of ever returning to zero.
Thanks a lot! |
|
x******a
发帖数: 6336 | 36 1-d random walk，原地不动的概率＝1／2. 往右的概率＝往左的概率＝1/4.
问在到10之前达到－5的概率。 |
|
f********k
发帖数: 136 | 37 4个random variable，每两个之间的correlation都一样，都是r，问r的取值范围。
可以想到的方法，用correlation matrix是semi positive definite这个性质，但这个
需要求一个4阶行列式，解一个4阶不等式，显然电面的时候没有时间这么做
第二种方法，根据绿皮书，两个RV之间的correlation类似于两个vector夹角取cos。所
以我们有4个vector，每两个夹角相同，极端情况是0度，所有vector重合，所以得到r
的最大值为1。但是我无论如何都画不出其他情况了，如何画4个vector，两两夹角相同
？3个vector的情况很简单，首尾相接的正三角形。但4个就不知道怎么画了，望高人指
点！
非常感谢！ |
|
m****r
发帖数: 141 | 38 关于绿皮书 random ants (p 102),
为什莫， 500 个 IID 随机变量 （with uniform distribution [0.1]）的期望值 是
499/500 ?
谢谢 |
|
L*******t
发帖数: 2385 | 39 版上有对Random Field Theory熟悉的兄弟么？
吼一声。。。 |
|
h****0
发帖数: 485 | 40 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？ |
|
s***h
发帖数: 662 | 41 consider a set of n processors, labeled p1, p2, ...pn. each trying to
broadcast a message. Time moves in discrete steps, and a processor will
succeed in broadcasting its message in step t if and only if no other
processors are trying to broadcast their messages in step t
since the processor cannot communicate directly, they try the following
randomized scheme to resolve contention. For a parameter m to be
determined later, they run a protocol that lasts for m consecutive phases,
each pha |
|
a********a
发帖数: 346 | 42 I have around 1000 obersvations in my data set. I want to randomly select
200 observations each time. How to write a R code?
My data like:
ID age Z1 Z2
1 20 0.5 3
Thanks a lot. |
|
j********g
发帖数: 49 | 43 【 以下文字转载自 Mathematics 讨论区 】
发信人: jinanddong (辐射), 信区: Mathematics
标 题: 知道random process (X+Y) 和 X 的distribution, 如何得到 Y?
发信站: BBS 未名空间站 (Sun Nov 16 00:46:53 2008)
现在我有两组实验数据, 可以分别画出两组数据的cummulative distribution
function (CDF). 假设一组是X, 另一组是X+Y, X 是不要的那部分, 请问如何得到y
的distribution?
Y最终是要用于simulation的, 所以不一定要精确的distibution, 只要知道每个P(Y=y)
, 就可以了. |
|
j*****e
发帖数: 182 | 44 Suppose your data has 1000 observation. You want to draw a sample of 100.Use
the following SAS code,
proc surveyselect data=dataname method=urs SAMPSIZE=100 rep=1 out=sample
seed=1594 outhits;
run;
There are other methods to randomly select observations (w or w/o
replacement, stratified sampling, clustered sampling, PPS sampling, etc).
Read SAS help for more detail. |
|
l******1
发帖数: 292 | 45 Is a random sample always necessary for methodologically sound health
promotion research?
why ？谢谢大家！ |
|
m********t
发帖数: 814 | 46 非统计背景菜鸟请教∶
有没有详细讲random field with homogeneous increment
of order n 的呀？谢谢啦 |
|
d******a
发帖数: 15 | 47 我也花了不少时间在RANDOM FIELD, 有些地方还是不明白 |
|
d******a
发帖数: 15 | 48 我也花了不少时间在RANDOM FIELD, 有些地方还是不明白 |
|
y****2
发帖数: 34 | 49 random field 是个蛮大的方向，不知道你这个是用在什么领域的？ |
|
o******6
发帖数: 538 | 50 ☆─────────────────────────────────────☆
davidmtl8 (davidmtl) 于 (Mon Feb 11 13:34:55 2008) 提到:
请问一个问题, two random variables x and y (do not know distributions of x
and y)
what is mean of (x/y), mean of ((x/y)2)
and variance of (x/y)
希望给些详细的说明,我是菜鸟一个.
谢谢
☆─────────────────────────────────────☆
davidmtl8 (davidmtl) 于 (Mon Feb 11 13:45:17 2008) 提到:
假设已知 mean of x and y, variance of x and y and covariance of (x,y)
ask for mean of (x/y), mean of ((x/y)2) and variance of (x/y)
☆────────────── |
|
