Random Definition and 1000 Threads

The discrete random variable K has the following PMF: p(k) = { 1/6 if k=0 2/6 if k=1 3/6 if k=2 0 otherwise } Let Y = 1/(1+K), find the PMF of Y My attempt: So, I am really confused about what this is asking. I took...

Homework Statement A standard procedure for finding an approximate mean and variance of a function of a variable is to use a Taylor Expansion for the function about the mean of the variable. Suppose the variable is y, and that its mean and standard deviation are "u" and "o". f(y) = f(u) +...

Homework Statement Let ##X_k## be iid uniform discrete on ##\{0,...,9\}##. Find the distribution of ##\sum\limits_{k=1}^{\infty} \frac{X_k}{10^k}##Homework Equations The Attempt at a Solution I've tried a lot of things, I've tried decomposing ##X_k## into 10 bernoulli trials, I've tried using...

So this is taken from another forum that I frequent. Basically just post any random old thought that you might be feeling. This way you don't have to start a whole new topic just to say "Damn it's cloudy out today". If you guys don't approve of the thread, then by all means please do...

How do I estimate the pdf from a random variable \(X\) where \(X = U_1 - U_2\) and \(U_i\) are uniform random variables? In the code below, I used unifrnd(-5, 5, 1000, 1) which generated a 1000x1 vector of uniform random number between -5 and 5. How do I estimate the PDF for X? rng; X =...

Homework Statement please refer to the question, i can't figure out which part i did wrongly. i 'd been looking at this repeatedly , yet i can't find my mistake. thanks for the help! the correct ans is below the question. where the c= 283/5700 , q = 179/5700 Homework Equations The...

(SOLVED) How to build a 3D random vector perpendic. to another vector Hi everybody, do you have an efficient method for build up a vector with random components which is perpendicular to another (unitary) 3D vector ? Context: I have to randomly select polarization vector (P) for...

Does "random" have different meaning in classical physics from SR, GR or QM? What is the difference between random, deterministic and probabilistic? Is probabilistic either random-probabilistic or deterministic-probabilistic, or is probabilistic a truly separate category on its own? If we...

Please realize I'm going to talk about random made up thoughts so don't take them too seriously, also I'm going to make a lot of wrong assumptions so be careful. Just a question, wouldn't it be OK to say time is a side effect of energy? It kind of makes sense because we humans really can...

[SIZE="2"]Unfortunately I did not find suitable section to post this topic, if there is suitable one you may move it there. It is shown in the science documentary film “Through the Wormhole” (Season 2, episode 5 called "Is There a Sixth Sense?") how the consciousness acts on the Random...

I have some confusion about multiple scattering. We always say that the problem of single scattering is always deterministic in nature.But while modeling the problem of multiple scattering, we take that the problem is stochastic in nature. I don't understand why. Why multiple...

Suppose X ~ U[ 0, pi ] What is the distribution of Y=sinX. I have a solution in my notes however I don,t understand the following the second transition: F_Y(y) = P(Y \leq y) = P(X \leq \arcsin(y)) + P(X \geq \pi - \arcsin(y)) = ... Where the P(X \geq \pi - \arcsin(y)) comes from?

Consider a one-dimensional random walk on the integer lattice, starting at 0. The next step is decided to be +1 or -1 with equal probability 0.5. The hitting time (the expected time required for the random walk to reach any integer α -- also called the first-passage time) will be...

Hello, I'm trying to write a monte carlo simulation for an optical analysis. Half the area of a sphere is within 60 degrees of the poles. Hence, I'm assuming half of randomly directed radiation should fall within 60 degrees of the poles, when radiation is generated at the center of the...

Of the 32 teams that qualify for the world cup (8 groups with 4 teams each), what percentage would a roster of 16 teams-to-advance-to-the-2nd-round (2 teams from each of the 8 groups) should be correct if the teams were chosen at random? Some background: A group of us at work filled out...

For example tritium has a half life of of 12.3 years. So if you had 2 atoms of tritium then after 12.3 year you would expect to have 1 atom of tritium and 1 atom of h-3. My question is, is it possible that tritium could decay in 1 second? Or how about 1 eon? I know its not probable but is it...

I don't understand, if everything in this world is relative to something else, then cannot we essentially say that nothing exists independently? We say that the universe is considered to be the ultimate 'background'. However, if we say it is expanding, shouldn't it be expanding relative to...

Hi My FORTRAN is rusty and my brain is even more rusty. I want to populate an annulus with a randomly distributed set of points. Any hints or tips to get me thinking about this would be gratefully received. Thanks D

This problem: A random variable X has expected value E(X) = 6.2 and variance Var(X) = 0.8. Calculate the expected value of g(X) where g(x) = 7x + 2. Do I just plug in numbers here? I've never seen this kind of problem before.

For the following probability density function: f(x) = [(x^2)/9] between 0 <= x <= 3 0 otherwise calculate the expected value E(X) of this distribution, and also calculate the variance I know I have to integrate the function but I don't know what else. Thanks!

Hi! I'm taking my first course in statistics and am hoping to get some intuition for this set of problems... Suppose I have a bowl of marbles that each weighs m_{marble}=0.01 kg. For each marble I swallow, there is a chance p=0.53 that it adds m_{marble} to my weight, and chance 1-p that...

Hello! My problem consists of : there is a representation of an uneven surface in terms of Fourier series with random coefficients: The random coefficients are under several conditions: W - function is undefined. Maybe you've confronted with such kind of expressions. The...

Can we calculate the electric field at any given point in space even if there are no charged particles there? The equation for electric field given in a standard EM course is kqq0/q0r^2 where q0 is a test charged impacted by the electric field. How about just any point in space?

suppose you have two random variables X and Y which are independent, we want to form a new random variable Z=XY, if f(x) and f(y) are density functions of X and Y respectively what is the density function of Z? I tried taking logs and applying convolution, but it did not really work

Pretty theoretical question here. I was talking with one of my friends the other day about a basic statistics problem that utilizes random variates. The problem asked us to perform 20 simulations of the world series final using a U(0,1) distribution. One team was given a probability of winning a...

Homework Statement If X is a random variable uniformly distributed over (0,1), and a, b are constants, what can you say about the random variable aX + b? What about X^2? Homework Equations For uniformity of notation, let f(x) = probability density function of x F(a) = distribution function...

Hi everybody. I am in this computer software class and I have a quiz coming up. My professor gave us a list of what to expect on the quiz and this question came up: Given a family of functions f1, f2, f3, .., fn and given a function f, find the best approximation of f by the family...

Hello, I've come across equations where people use the approximation \int_0^1 \exp(f(x))\, dx \approx \exp \left( \int_0^1 f(x)\, dx\right) I can see that this is correct if f(x) is small, one just uses exp(x) = 1+x+... However, it appears that this approximation has a broader validity...

Suppose we have a function ##F:\mathbb{R}_+\to\mathbb{R}_+## such that ##\frac{F(y)}{y}## is decreasing. Let ##x## and ##y## be some ##\mathbb{R}_+##-valued random variables. Would ##\mathbb{E}x\leq\mathbb{E}y## imply that ##\mathbb{E}F(x)\leq\mathbb{E}F(y)##?

A cone's volume with height ##x## and radius ##y## is ##1/3## of the volume of a cylinder with height ##x## and radius ##y##.I was trying to visualize it in my head and struggled a bit.Take a rectangle triangle with height ##x## and the other side of length ##y## which isn't the hypothenuse ...

I am looking at an object that diffuses randomly inside a circular plane. What is the easiest way to find the expectation value for how long would it take on average to reach the wall if it was initially placed at a random position? If it is easier: what if the initial position were the...

I am trying to derive the distribution for the sum of two random vectors, such that: \begin{align} X &= L_1 \cos \Theta_1 + L_2 \cos \Theta_2 \\ Y &= L_1 \sin \Theta_1 + L_2 \sin \Theta_2 \end{align} With: \begin{align} L_1 &\sim \mathcal{U}(0,m_1) \\ L_2 &\sim...

Homework Statement Let X and Y be rv's with joint pdf f(x,y) = 6(1-y) for 0≤x≤y≤1 and 0 elsewhere find Pr(X≤3/4, Y≤1/2) Homework Equations The Attempt at a Solution Ok I am having trouble with finding the right limits of integration for dependent variables. If we let the...

Homework Statement I want to find the PDF for arccos and arcsin of a uniform random number. Given: Y\sim\mathcal{U}(0,2\pi) \\ X = cos(Y) The Attempt at a Solution I started with trying to find the CDF: \begin{align} F_X& = P(X \le x) \\ & = P(cos(Y) \le x) \\ & = P(Y \le arccos(x))...

In order to help with server load, we are splitting up the larger threads. This is a continuation of Random Thoughts Part 2 thread located here https://www.physicsforums.com/showthread.php?t=687099&page=186

Homework Statement |zi - 3| = Pi Homework Equations Well, it clearly has to do with a circle but I do not believe there is a general equation for what I am asking about. The Attempt at a Solution There is no general solution not trying to solve anything. I want to know exactly...

Homework Statement Let ##Y_1,...Y_n## be independent standard normal random variables. What is the distribution of ##\displaystyle\sum_{i=1}^n{Y_i}^2## ? Let ##W_n=\displaystyle\frac{1}{n}\sum_{i=1}^n {Y_i}^2##. Does ##W_n\xrightarrow{p}c## for some constant ##c##? If so, what is the...

How to transform a random variable CDF to a standard normal Given F(x) = 1- exp (-sqrt x), for x greater that 0 Thanks.

Homework Statement I am attempting to calculate a heat transfer across a medium with known material properties. I have the equation and all but one variable I have an exact answer for. I require the variance of my answer. Homework Equations I know ALL variables (ie numerical value) except...

Homework Statement Let X and Y be random losses with joint density function f(x,y) = e^-(x + y) for x > 0 and y > 0 and 0 elsewhere An insurance policy is written to reimburse X + Y: Calculate the probability that the reimbursement is less than 1. Homework Equations Have not...

Hello All! A recent problem has stuck with me, and I was hoping you could help me resolve it. Consider the following premise: Let us assume that X \sim \mathcal{U}(-3,3) (U is the continuous, uniform distribution). And let the transformation Y be applied thus: Y = \left\{ \begin{align*} X+1...

Code: Random number less than specifed value This isn't really a homework problem. I'm just doing this for fun and giggles. But given the nature of the forum rules, I'll post it here. Homework Statement Create a method (function) that returns a random number less than the specified...

Homework Statement If the probability density function(p.d.f.) of a random variable X is f(x) = 1/6 * e-|x|/3 where x is lying in (-∞,∞) and |-x| = x if x≥0, then what is the p.d.f. of the random variable Z = XY = X*|X| where Y = |X| ? Homework Equations Nothing special. The Attempt at a...

Hi everyone, sorry to bother you with a really random question, and I hope I'm posting this in the right board, but here goes anyway... The universe is currently too small in size to write out an entire googolplex. The visible universe is 4 x 1080 m3 (according to the ever reliable Wikipedia...

Let $\Omega=\{\omega_1,\omega_2,\omega_3\}$ an sample space, $P(\omega_1)=P(\omega_2)=P(\omega_3)=\dfrac{1}{3},$ and define $X,Y$ and $Z$ random variables, such that $X(\omega_1)=1, X(\omega_2)=2, X(\omega_3)=3$ $Y(\omega_1)=2, Y(\omega_2)=3, Y(\omega_3)=1$ $Z(\omega_1)=3, Z(\omega_2)=1...

Hello, I have two random variables X and Y that can take values of the kind (a,b) where a,b\in \{ 0,1,2,3 \}. Thus, the sample space has only 16 elements. I have, say, N observations for both X and Y, and I would like to know if there is some correlation between X and Y. - How is this...

Hey! I've been doing some research on random walks. From what I have gathered, a random walker in 1-D will have: <x> = [FONT="Georgia"]N l (2 p - 1) σ =[FONT="Georgia"] 2 l sqrt[N p (1 - p) ] Here, N is the number of steps, p is the probability to take a step to the right and l is the step...

Homework Statement I have a physical system, which I know the time average statistics. Its probability of being in state 1 is P1, state 2:P2 and state 3:P3. I want to simulate the time behavior of the system.Homework Equations N/AThe Attempt at a Solution I assume the rate of transition event...

Homework Statement What is the expected value of ||Ax+n|| where || || is the L2 norm and x and n are uncorrelated and E[n] = 0 The Attempt at a Solution E[ norm of Y] = E[(Ax+n)' (Ax+n)] = E[(x'A'+n')(Ax+n)] = E[x'A'xA +x'T'n +n'Ax +n'n] the three last terms = 0 due to...

Homework Statement Find the conditional distribution function and density for the random variable X defined on R given that X is in some interval I = (a,b) where P(X in I) > 0. Assume that the density and distribution for the random variable X is known Homework Equations fX|X\inI =...