Random Definition and 1000 Threads

I'm new to the electrical engineering field and need guidance on how I can program a PIC (PIC12F675P) controller to generate random high/low frequency noises through a amplifier (TDA2822M). The sounds I'm aiming for need to be similar to those generated by a dial up modem. I will appreciate...

Homework Statement If Y=X1+X2+...+XN prove that <Y>=<X1>+<X2>+...+<XN> Homework Equations <Y>=∫YP(Y)dY over all Y. The Attempt at a Solution I only seem to be able to show this if the Xi are independent, and I also think my proof may be very wrong. I basically have said that we can write the...

Time to split the thread again. Here is the link to the old thread. https://www.physicsforums.com/threads/random-thoughts-part-three.745013/

Homework Statement Z = X - Y and I'm trying to find the PDF of Z. Homework Equations Convolution The Attempt at a Solution Started by finding the CDF: Fz(z) = P(Z ≤ z) P(X - Y ≤ z) So I drew a picture So then should Fz(z) be: since, from my graph, it looks as though Y can go from...

Hi guys, I need help with this question. Suppose X has a normal distribution with mean u1 and known standard deviation 7. Suppose Y has a normal distribution with mean u2 and known standard deviation 9. Suppose we have a random sample of size 6 from the X distribution. The sample mean xbar is...

Does anyone know where I can go to figure out how to generate a random 3-4 letter sequence BUT with every click that sequence is stored in an array and can not come up again?

Homework Statement Let X denote a continuous random variable with probability density function f(x) = kx3/15 for 1≤X≤2. Determine the value of the constant k. Homework Equations I'm not sure if this is right but I think ∫kx3/15 dx=1 with the parameters being between 2 and 1, The Attempt at a...

Homework Statement If X is uniformly distributed over (0,1), find the PDF of Y = |X| and Z = e^X Focusing on the |X| one Homework Equations Derivative of CDF is the PDF The Attempt at a Solution So I start by writing down the CDF of X, Fx(x): 0 for x <0 x for 0 ≤ x ≤ 1 1 for x ≥ 1 And I...

Homework Statement Here's the problem with the solution provided: Homework Equations Fundamental Theorem of Calculus (FToC) The Attempt at a Solution So I understand everything up to where I need to take the derivative of the integral(s). Couple of things I know is that the derivative of...

Homework Statement If ##X\sim\mathcal{U}(-1,1)## and ##Y = X^2##, is it possible to determine to ##cov(X, Y)##? Homework Equations \begin{align} f_x &= \begin{cases} 1/2, & -1<x<1\\ 0, & \text{otherwise} \end{cases}\\ f_y &= \begin{cases} 1/\sqrt{y}, & 0<x<1\\ 0, & \text{otherwise} \end{cases}...

We have a r.v. X with p.d.f. = sqrt(θ/πx)*exp(-xθ) , x>0 and θ a positive parameter. We are required to show that 2 θX has a x^2 distribution with 1 d.f. and deduce that, if x_1,……,x_n are independent r.v. with this p.d.f., then 2θ∑_(i=1)^n▒x_ι has a chi-squared distribution with n...

Given a Bernoulli r.v., W, which is derived from r.v. T(Poisson) (a)if T=0 then W=1 and b) if T>0 then W=0). One has to show that the sample mean (the proportion of 0s in the sample), is an unbiased estimate of φ=e^λ. Also, how does one find the variance of the sample mean and show that this...

If one has a Bernoulli random variable W that is derived from a Variable T (Poisson λ), by the following rules W = (if T=0 then W=1 and if T>0 then W=0), I am having trouble finding the pf for W. Any suggestions about how to proceed forward?

So, I have a jokester (MHB user Cmoney) in my class (what teacher doesn't?), who decided to go all-out on a quiz question. The question reads as follows: You are planning a report on apartment living in a college town. You decide to select three apartment complexes at random for in-depth...

Homework Statement The components of a random vector ##\mathbf{X} = [X_1, X_2, \ldots, X_N]^{\intercal}## all have the same mean ##E_X[X]## and the same variance ##var(X)##. The "sample mean" random variable $$ \bar{X} = \frac{1}{N}\sum_{i = 1}^NX_i $$ is formed. If the ##X_i##'s are...

Hi, I am having a hard time understanding why the Addition Rule for two Random Variables holds even when the random variables are dependent. Essentially: why is E(X+Y) = E(X) + E(Y) when X and Y are dependent random variable? Given the two variables are dependent, if X happens to take on a...

Hi all I am doing this question right now and I don't even know how to start it up. I know that it's in relation to a sum of a random number of random variables, but I don't know how to continue on from that. I've read my textbook and it states some definition for an MGF which is: $M_{y}(t) =...

Homework Statement Determine the minimum mean square error for the joint PMF. You will need to evaluate ##E_{X, Y}[(Y - 14/11\cdot X - 1/11)^2]##. Homework EquationsThe Attempt at a Solution The answer is ##\frac{3}{22}##, but when I work it out, I get ##\frac{203}{484}##. From my values, I...

With a Poission random variable, we know that \(E[X] = var(X) = \lambda\). By definition of the variance, we can the second moment to be \[ var(x) = E[X^2] - E^2[X]\Rightarrow E[X^2] = var(X) + E^2[X] = \lambda(1 + \lambda). \] The characteristic equation for the Poisson distribution is...

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...

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 number...

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...