Random Definition and 1000 Threads

Homework Statement Let X ~UNIF(0,1), and Y=1-e-x. Find the PDF of Y Homework Equations The Attempt at a Solution So i have Fy=Pr(Y<y) =Pr(1-e-x<y) =Pr(-e-x<y-1) =Pr(e-x>1-y) =Pr(-x>ln(1-y)...

Homework Statement 10 face cards are face down in a row on a table. Exactly one of them is an ace. You turn the cards over one at a time, moving from left to right. Let X be the random variable for the number of cards turned before the ace is turned over. What is the probability function...

Can anyone help me with the below question? for each of the following pairs of random variables X,Y, indicate a. whether X and Y are dependent or independent b. whether X and Y are positively correlated, negatively correlate or uncorrelated i. X and Y are uniformly distributed on the disk...

Homework Statement Given: The joint probability distribution function of X and Y: f(x,y) = 2xe^(-y), x > 0, y > x^2 0, otherwise Obtain the pdf of V = (X^2)/Y The Attempt at a Solution The interval of V is (0,1) because Y is always...

Homework Statement Suppose that X is uniformly distributed on (0,2), Y is uniformly distributed on (0,3), and X and Y are independent. Determine the distribution functions for the following random variables: a)X-Y b)XY c)X/Y The Attempt at a Solution ok so we know the density fx=1/2...

Playing around with Wolfram Alpha I discovered an elegant looking little equation. Judging by the decimal approximation of both sides, there seems to be an extremely high probability that it is true. A picture of the equation is attached but ill try to type it too...

Is it wrong to say that QM is random? Aren't we too ignorant of what's going on at the level of QM to claim with certainty what's going on? How could the Universe be deterministic at the level of GR, but we different at the level of QM. They are both connected, only describing different scales.

Homework Statement Let the random variable X represent the length of the side of a square. It has a uniform distribution over the interval (0, 5). What is the cumulative distribution function for the area of the square, Y? Homework Equations F(x) = 0.2x (the cdf of the side). The...

In an analog to digital conversion and analog waveform is sampled, quantized and coded. A quantized function is a function that assigns to each sample value x a value y from a generally finite set of predetermined values. Consider the quantized defined by g(x)=[x]+1, where [x] denotes the...

I am not a physics student - I am a science fiction writer. But an idea is puzzling me, and I will attempt to convey it. However, I apologise if my terminology or an incorrect understanding of things makes my question unclear. Firstly, I am under the impression that the laws of physics do...

Hi guys, I have a question re: random numbers and probability. If I have a random number generator that generates a number between 1 and 10, and say I generate a kazillion of these numbers, then doesn't each number have the same probability of showing up? So then, after a kazillion numbers, I...

Homework Statement [/b] There are two problems I need help with, which are posted below. Any help is appreciated. 1)Let X have a Poisson distribution with parameter λ. If we know that P(X = 1|X ≤ 1) = 0.8, then what is the expectation and variance of X? 2)A random variable X is a sum of...

Homework Statement Consider independent random variables X1, X2, X3, and X4 having pdf: fx(x) = 2x over the interval (0,1) Give the pdf of the sample maximum V = max{X1,X2,X3,X4}. The Attempt at a Solution I can't find ANYTHING about how to solve this in the book, please help!

Two "Sum of Random Variables" Problems Homework Statement Problem A: Consider two independent uniform random variables on [0,1]. Compute the probability density function for Y = X1 + 2X2. Problem B: Edit: never mind, solved this one Homework Equations fY(y) = F'Y(y) FY(y) = double integral...

If X is some RV, and Y is a sum of n independent Xis (i.e. n independent identically distributed random variables with distribution X), is the mean of Y just the sum of the means of the n Xs? That is, if Y=X1+X2+...+Xn, is E[Y]=nE[X]? I know that for one-to-one order-preserving functions, if...

Homework Statement Consider the following probability table: X 1 2 3 4 P(X) 0.4 0.25 0.25 0.1 Use the rejection method to generate a random number. Use the following list of random numbers: 0.6072, 0.4893, 0.0899, 0.3456, 0.4419...

Homework Statement Z is a random variable. P(X=a) = p1 P(X=b) = p2 P(X=c) = p3 P(X=d) = p4 Find the variance. Homework Equations Var(X) = E(X2) - E(X)2The Attempt at a Solution Okay so for the E(X2), I am currently very confused. My professor gave us this formula where E(X^2) =...

hello, i made this account just so i could figure this out--i realize people often do that (to make an account without an initial intention of becoming a regular), so i apologize for that; if you feel i am taking advantage of your time and expertise, then i understand. but i am not trying to...

n is the population p is the probability for one person to be sick y is the numbers who are sick I want to use R to generate random y. Binomial distribution. Does anyone know which command?

Homework Statement Find the exact value of P(|Y- μ| < 1.4σ) for an exponential random variable with parameter β. Homework Equations The only equation that I can think of is the exponential distribution equation: ∫(1/β)e^(-y/β) The Attempt at a Solution I have been unable to...

Homework Statement The random variables X1 and X2 are independent and identically distributed with common density fX(x) = e-x for x>0. Determine the distribution function for the random variable Y given by Y = X1 + X2. Homework Equations Not sure. Question is from Ch4 of the book, and...

Question about "random walk" Homework Statement . .. Recall that in a random walk where each step has length l, the total distance traveled after N steps is L = N1/2lHomework Equations The Attempt at a Solution My problem is the N number of steps, not sure how i would find that. I saw in the...

Hello! I want to know, how do we get (i mean how do we calculate) energy specters if we send random sound waves to a probe. Is there any Linux computer program capable of doing this? Regards Ziga

Homework Statement random variable of X has pdf: f(x) = (3/16)*x2 from interval (-2,2). Also, E(X) = 0, and E(X2) = 12/5. Find the pdf of Y = X2 Homework Equations The Attempt at a Solution I don't really know where to start.

Please give your definition of mathematical randomness. Consider what randomness is, as opposed to what it is not. Does randomness or order approach probability one as the number of samples approaches infinity? Is our universe globally and/or locally random? Are there different degrees...

hi, i have some question and i hope someone know answers: Lets have closed two dimensional space with some particles, which have random position and random velocities. In the center of space is object, which has central fixed axis. This object has no velocity and no angular velocity. (see...

Hello folks, this is my first post. I'm not quite sure that I fully understand the idea of a random walk of a photon that is generated at the core of a star. I've read this: http://www3.wooster.edu/physics/jrIS/Files/Walker_Web_article.pdf My understanding of the theory is this: A...

Homework Statement I am really tired of useing a calculator for small calculations. Are there any books out there that teach you how to mentally calculate quicker? This would save me time on tests and make things more efficient so if there are any books please let me know. thank you...

Hi, I am interested in the product of a Gaussian random variable with itself. If X is Gaussian then what is X^2? We know that the resultant variable of the product of two independent Guassian variables is still Gaussian but I am afraid that this is not true when you multiply it with itself. Is...

X is a random variable with a continuous distribution with density f(x)=e^(-2|x|), x e R How would you calculate E(e^(ax)) for a e R? Will it be right to take a certain range of a? And also, can you take the bounds for the integral to be between -Infinity and Infinity?

Homework Statement Consider a random variable X having cdf: 1, x ≥ 4, 3/4, 1 ≤ x < 4, FX(x) = 1/2, 0 ≤ x < 1, 1/4, −1 ≤ x < 0...

Bear with me, I am not a scientist. Also, this is NOT a question about free will. I wanted to know if particles ever move in random directions. Since I know there will be an issue of semantics here, I will give some examples: Two separate universes (when I say universe I mean, "area where stuff...

Hi there, As many texts' discussion, we usually use a variable x for any value randomly picked. For a Bernoulli trials, i.e. each random variable x can either be successful or fail. If the probability of success if p and that of failure is q=1-p, then the expectation value of x would be...

I am trying to create a list of 5 random numbers between 1 and 20 In[62]:= RandomInteger[{1, 20}, 5] Out[62]:= {10, 11, 9, 8, 1} But is it possible to exclude the number 10 from appearing?

"Random Phase Approximation" (Why they call it so?) Hi, I'm wondering that why the scientists call this phenomena in many body physics "Random Phase Approximation". (Why Random? Why Phase?) It seems that when we want calculate a correlation function in quantum field theory, it leads to...

HELP!Sums of Random Variables problem: Statistics Homework Statement 3. Assume that Y = 3 X1+5 X2+4 X3+6 X4 and X1, X2, X3 and X4 are random variables that represent the dice rolls of a 6 sided, 8 sided, 10 sided and 12 sided dice, respectively. a. If all four dice rolls yield a 3, what...

lets assume matrix A = [a]mxn and B = [b]nxp (AB)_{ij}=\sum_{r=1}^{n}A_{ir}B_{rj} why is that ? i guessed it would be (AB)_{ij}=\sum_{r=1}^{n}A_{ir}B_{jr} where m=p. so is there any logic behind that or its just random ?

If we have a person who in t=0 (time) is standing on x=0 . every one second (t=t+1) in without any dependency on previous steps : he moves to right(x=x+1) in probability = 1/4 and he moves to left (x=x-1) in probability = 1/4 . and he goes back to x=0 in probability = 1/2 . show that...

Homework Statement http://s359.photobucket.com/albums/oo40/jsmith613/?action=view&current=MathQUUU.pngHomework Equations The Attempt at a Solution So I know that k = 1 But if F(>3) = 1 then why does F(3) also equal 1 Thanks

Hello, I am given a random variable X with a p.d.f. fX(x;\theta) (depending on a certain deterministic parameter \theta) and I want to consider N sampled observations of that variable: x1,...,xN. Is it correct to consider each observation as a separate random variable xi with the same pdf...

Homework Statement find the characteristic equation of a binomial variable with pmf p(x) =\frac{n!}{(n-k)!k!}*p^{k}*(1-p)^{n-k}Homework Equations characteristic equation I(t) = \sump(x)*e^{tk}The Attempt at a Solution I(t) = \sum\frac{n!}{(n-k)!k!}*(p^{k}*(1-p)^{-k}*e^{tk})*(1-p)^{n} i am...

Homework Statement From past experience, a professor knows that the test score of students taking a final examination is a random variable with mean 65. Give an upper bound on the probability that a student's test score will exceed 75. Homework Equations None that I know of. The...

Homework Statement A trial consists of tossing two dice. The result is counted as successful if the sum of the outcomes is 12. What is the probability that the number of successes in 36 such trials is greater than one? What is this probability if we approximate its value using the Poisson...

Hey, In doing calculations on superconductors, I often hear that people say "averaging over the random potential of impurities make the theory translationally invariant both in time and space". I do not exactly understand it? Could you please explain it through a simple example or by citing a...

Hello, given a continuous random variable x with a known PDF, how can we determine in general the PDF of the transformed variable f(x) ? For example f(x)=x+1, of f(x)=x2 ... ? Also, if we have two random variables x,y and their PDF's, is it always impossible to determine the PDF of f(x,y)...

\mathrm{prob} \propto \mathrm{e}^{-\frac{(a -x_1)^2}{2 \sigma^2}} \mathrm{e}^{-\frac{(x_1 -x_2)^2}{2 \sigma^2}} \mathrm{e}^{-\frac{(x_2 -x_3)^2}{2 \sigma^2}} \mathrm{e}^{-\frac{(x_3 -b)^2}{2 \sigma^2}} a and b are known real constants. Is there a way to generate x_1, x_2, x_3 independently...

[b]1. The problem statement If i generate a list of 300 random numbers in excel, each number between 1-50 for example, and i plot the frequency that each number comes in a histogram, how can i tell, looking at the histogram, if the numbers are really random? is there a certain distribution...

Suppose X and Y are Uniform(-1, 1) such that X and Y are independent and identically distributed. What is the density of Z = X + Y? Here is what I have done so far (I am new to this forum, so, my formatting is very bad). I know that fX(x) = fY(x) = 1/2 if -1<x<1 and 0 otherwise The...

Hi, I would like to ask a question please. Assume we have a random vector X that is distributed under the Gaussian model and take the inner product of this vector and another constant vector d. Will the source distribution (Gaussian) remain the same? My intuition (although I might be...

hi all, i am a new member here. nice to meet you all. i remember seeing a derivation of diffusion equation from the equation of motion \dot{x}=\eta(t) where \eta(t) is white noise. i can't remember where i saw this... could anyone please help me on that? it should be something like...