Random Definition and 1000 Threads

Homework Statement This is an example in a textbook; it already has the solution. I don't understand how E[X|Y] was obtained though. So my question is how do I calculate E[X|Y] from the information given? http://img689.imageshack.us/img689/484/20120413134552578.jpg...

Homework Statement Stress : S(t) = a0 + a1X(t) + a2X2(t) where X(t) is the random displacement, a Gaussian random process, and stationary. 1) determine the PDF of S(t) 2) determine the joint PDF of stress and stress velocity, S(t) and S'(t). 3) how would you determine the PDF of...

Hi Guys, Long time reader first time poster... This simple question has stumped me all day and I think I've finally cracked it! I'm hoping someone can confirm that, or tell me how wrong I am - either is fine :) One in 1000 cows have a rare genetic disease. The disease is not contagious...

Hi folks, I need to evaluate (numerically) a multi-dimensional integral of the form \int_A f(x) dx. Now in my application, I already have points inside the domain A which are distributed like \frac{f(x)}{\int_A f(x) dx}. So I hoped I could use these random points in some importance sampling...

Here is the homework question. I only have an issue with part c but have shown all my work up until then. Any help is appreciated! Mr and Mrs Brown decide to continue having children until they either have their first boy or until they have five children. Assume that each child is equally...

I am developing a simple probabilistic model of my own mistakes in (1) solving math problems and (2) implementing algorithms on a computer. I have reduced the problem to one which seems simple enough, but which I have been unable to solve, due to my mathematical inexperience. I figured I would...

David C. White owns a small advertising business. He has twelve employees. The names of the employees are given below. 1. Becker 2. Brown 3. Chasten 4. Ito 5. Kim 6. Spitzer 7. Taylor 8. Walt 9. Wang 10. Zhang 11. Zhao 12. Zhu Use the list of random digits below to select...

Edit: I have to think more about this, I'll post later.

Hi, Apologies that this is basic question but I have to start somewhere! (-: The problem is succinctly stated in the msg title but, in greater detail; I'm working with some biological data from which samples have been taken. The sampling should have been at random. The samples include...

Homework Statement A submarine has three navigational devices but can remain at sea if at least two are working. Suppose that the failure times are exponential with means 1 year, 1.5 years, and 3 years. What is the average length of time the boat can remain at sea?Homework Equations Density...

I would like to know the distribution of z as the euclidean distance between 2 points which are not centred in the origin. If I assume 2 points in the 2D plane A(Xa,Ya) and B(Xb,Yb), where the Xa~N(xa,s^2), Xb~N(xb,s^2), Ya~N(ya,s^2), Yb~N(yb,s^2), then the distance between A and B, would be...

Homework Statement So, I know the pdf for independent random variables is found by using the convolution; the pdf is f[sub:X+Y](a) = ∫ f[sub:X](a-y)f[sub:Y](y)dy, but can I just use the density function for a function of a random variable instead; that is: f[sub:X+Y](x[u,v], y[u,v])(Jacobian...

Homework Statement Two variables, X and Y have a joint density f(x,y) which is constant (1/∏) in the circular region x2+y2 <= 1 and is zero outside that region The question is: Are X and Y independent? Homework Equations Well, I know that for two random variable to be independent...

Homework Statement let x_{i} be a random variable, and let y_{j} = \sum x_{i}. The variance of the random distribution of the x_{i}'s is known, and each y is the sum of an equal amount of x_{i}'s, say N of them. How do I compute the variance of y in terms of \sigma^2_{x} and N? Homework...

Hello Everyone :) I have been facing a little difficulty when encountering such kind of problems . i have also written down my line of thinking and approach which i take to solve them. So, please try to give me the correct line of thinking while solving such problems: 1. If A is invertible...

I've been struggling with this problem for about two weeks. My supervisor is also stumped - though the problem is easy to state, I don't know the proper approach to tackle it. I'd appreciate any hints or advice. Let V be an random k-dimensional vector subspace of ℝn, chosen uniformly over...

Hey everyone. I haven't taken statistics yet, but as a matter of interest I was contemplating the fact that uniform random variables added together seem to generate "bell curve" like distributions. My question is if I add up an infinite number of equally distributed random variables will the...

I have two multivariate normally i.i.d random variables, x and y, that are size n vectors. Let us assume for simplicity that their variances are 1. From these random variables, I form two vectors that contain their means, and denote these mx and my. I know that if mx = my, then W = (mx -...

Is an infinite series of [nonrepeating] random numbers possible? That is, can the term "random" apply to a [nonrepeating] infinite series? It seems to me that Cantor's logic might not allow the operation of [nonrepeating] randomization on a number line approaching infinity.

Hi all I was wondering if anybody knew any good books (preferably textbooks) on random matrix theory? thanks in advance.Edit: My apologies if this is posted in the wrong section.

[b]1. X_1,X_2\cdots X_n\:\text{are IID Random Variables with CDF}\,F(x)\:\text{and PDF}\,f(x)\\ \text{then What is the CDF of Random variable }\,Max(X_1,X_2\cdots X_n) Homework Equations [b]3. \text{Since Y will be one among}\,X_1,X_2\cdots X_n,\text{why cannot its CDF be }\,F(x)\\\text{I need...

I have some questions I could not find answer I hope here to get the correct answer my questions here in this picture ( attached ) 2 questions

1. Homework Statement During a typical Pennsylvania winter, I80 averages 1.6 potholes per 10 miles. A certain county is responsible for repairing potholes in a 30 mile stretch of the interstate. Let X denote the number of potholes the county will have to repair at the end of next winter. 1...

Hello there, lets say i have a harmonic oscillator equation d^2x/dt^2 = -w^2 x = -Asin(wt) w=frequency, A=amplitude..how can i plot this equation for w^2=1, x(0)=1? and what if the equation contains random number d^2x/dt^2 = -w^2x+Bn, n=gaussian random number with mean value equal to zero...

I know the E[X] = Integral between [-inf,inf] of X*f(x) dx Where X is normally distributed and f(x) is the PDF How do I find the expectation of X4? Bare with me because I'm useless in Latex So far what I've done is written the integral as Integral between [-inf,inf] of X4*f(x) dx...

Homework Statement During a typical Pennsylvania winter, I80 averages 1.6 potholes per 10 miles. A certain county is responsible for repairing potholes in a 30 mile stretch of the interstate. Let X denote the number of potholes the county will have to repair at the end of next winter. 1...

Homework Statement 1. A test consists of 10 true-false questions. (a) In how many ways can it be completed? (HINT: The task of completing the test consists of 10 stages. Use the Product Rule.) (b) A student answers the questions by flipping a coin. Let X denote the number of correctly...

Homework Statement There is a population of 30 elk. 6 elk are captured, tagged and then released into the wild. Then later 5 elk are captured, what is the probability that k elk are tagged? Homework Equations p=6/30 = 1/5P = \stackrel{n}{k} * pk * (1-p)k \stackrel{n}{k} is n...

How can a random distribution relate to a non-random one?

I'm a huge noob and I don't know much about physics and space and stuff, but I was thinking about this in the shower today.. Anyone care to comment? Or correct me on anything? Ok, so I was talking about to Daniel about Gravity, the Sun, and Black Holes.. (Yes we are ghetto nerdy xD) And i...

Homework Statement Find the Mean and Variance of Random Variable Z = (5x+3) Using data set:Using: & The Attempt at a Solution

I hope I wrote that correctly but I'm trying to find the joint. I heard it was impossible from someone. X = A/R A~BIN(n1, p1) R~BIN(n2, p2) I know I shouldn't be using the Jacobian method for Discrete distributions but I have to do it anyway. Anyone know?

Hi, I'm looking at how to derive the mean-squared-distance from the velocity autocorrelation for a random walk. It is given on this page: http://www.compsoc.man.ac.uk/~lucky/Democritus/Theory/msd2.html Near the middle of that page the author says 'defining u'=u+s and integrating over u, results...

What is the probability that a number selected from 0-9 will be the same number as one randomly selected from 0-4? Relevant equations: $$P(A \cap B) = P(A)*P(B|A)$$ I used the equation above, using A as the event that the number selected from 0-9 will be between 0 and 4, and B as the event that...

What is the general equation of a random walk with : a) modified random walk b) absorbing barriers c) simple symmetric

(1)Consider the expected duration of the modified random walk. Show that conditioning on the first step produces a recurrence equation of the following form. Ea = ˜pEa+1 + ˜qEa−1 + ˜c. (2)Clearly identify the values of ˜p, ˜q and ˜c in terms of p, q and r...

1. Imagine a positive point x not equal to zero. 2. Consider a randomly chosen point y with distance to zero less than x. 3. Let y=x. Repeat #2. 4. Is the sum of the y-values finite as y approaches zero?

Let X_1, X_2, ... be a sequence of random variables and define Y_i = X_i/E[X_i]. Does the sequence Y_1, Y_2, ... always convergence to a random variable with mean 1?

i am tying to analyze a random walk on an integer lattice \mathbb{Z}^k. for k=1, what is the probability that after steps the drunkard's distance from the origin is lower than \sqrt{n}?

This just came into my head. I don't think I really understand the significance of Maxwell's demon. Please don't try to explain it to me. It's just a random thought.

Hello there, I am wondering if somebody could help in an issue far from my expertise. I have some data which is reasonable to conjecture could be modeled with a random walk with drift. I am struggling though to understand how to estimate from the empriic data the most likely drift and...

Dears, If a random variable is generated with the pdf of p(f) = 1/(f^x), how can I derive the upper bound or lower bound of the random variable? Thanks,

Dears, If a random variable is generated with the pdf of p(f) = 1/(f^x), how can I derive the upper bound or lower bound of the random variable? Thanks,

Let be $X_1, X_2, ..., X_n, ... $ independent identically distributed random variables with mutual distribution $ \mathbb{P}\{X_i=0\}=1-\mathbb{P}\{X_i=1\}=p $. Let be $ Y:= \sum_{n=1}^{\infty}2^{-n}X_n$. a) Prove that if $p=\frac{1}{2}$ then Y is uniformly distributed on interval [0,1]. b) Show...

I am wondering if I can find a decomposition of Y that is absolutely continuous nto two i.i.d. random variables X' and X'' such that Y=X'-X'', where X' is also Lebesgue measure with an almost everywhere positive density w.r.t to the Lebesge mesure. My main intent is to come up with two i.i.d...

given the following Probability density function: f x,y(x,y) = { 0.5, ( 0<y<1, 2y-x<2, 2y+x<2 } 0, else and i need to find f z(z) while z=y-x i got really confused while trying to calculate the borders of x and y for the integration. i would be really thankful for someone explaining...

Given the fact that X and Y are independent Cauchy random variables, I want to show that Z = X+Y is also a Cauchy random variable. I am given that X and Y are independent and identically distributed (both Cauchy), with density function f(x) = 1/(∏(1+x2)) . I also use the fact the...

Hello, I don't really know if this is considered a challenging problem but this is not for homework: You're given a set of numbers S of size n. From S, you draw a random sample A, |A| < n. From S, you draw a random sample B, |B| < n. Sampling doesn't remove items from S. What is the...

Dear All, I am simulating a random walk on a sphere with unit radius. I want to move from current location p_t to the new location p_{t+1} along the big circle, whose arc has an angle omega relative to p_t's latitude. I tried using the law of cosine. But at the poles, the law of cosine...

One day I just put on my polarized sunglasses, and on the road, I looked at cumulonimbus cloud probably in the congestus stage in a system with many other cumulus clouds (those big puffy clouds), and a single giant cumulus cloud appeared yellow-ish when wearing the polarized sunglass, and I took...