Random Definition and 1000 Threads

I want to find the probability density function (pdf) of the difference of two RV's, p_{\Delta Y} = p_{(Y_1 - Y_2)},where y = \sin \theta, and where \theta_1 and \theta_2 are random variables with the same uniform distribution p_{\theta}=\mathrm{rect}\left(\frac{\theta}{\pi}\right). This has...

This problem appeared in a problem set which I encountered on the internet In a game, balls are labeled by integer numbers. One chooses three different integer numbers between 1 and 10. Two balls are picked at the same time, at random from a box. If they are part of the three earlier chosen...

Pick a random set of N points from the unit disc. Calculate the distance between all pairs of points and call the smallest value r. Do this calculation for many such sets. Please give me a hint how to estimate what the average value of r is. I guess a computer program could quickly come up with...

Homework Statement If the random variables T and U have the same joint probability function at the following five pairs of outcomes: (0, 0), (0, 2), (-1, 0), (1, 1), and (-1, 2). What is the covariance of T and U? Homework Equations σxy = E(XY) - μx⋅μy The Attempt at a Solution My issue with...

Hi Imagine we have a lottery, with chance of winning 1 in 1000 (1/1000). I have made computer simulations in order to find confidence levels for winning. At 1000 bought lottery tickets, the confidence of winning is 64.1% and 2000 bought lottery tickets the confidence of winning is 87.1% By...

typical random walk : one step forward or backward with equal probability and independence of each step , what is the expectation and Variance . so i define indicator variable xi ={1 or -1 with equal probabilty . E(xi) = 0 Var(xi) = 1 now define Sn as the sum of i=1,...,n each step is...

https://ibb.co/guBuPd As the title indicates, I want to calculate the Probability of a stock price reaching a determined point, by considering the system as a random walk model, and after that, to compute the so called "maximal curves". I found the whole explanation in this article...

Homework Statement I am trying to understand the very last equality for (let me replace the tilda with a hat ) ##\hat{P_{X}(K)}=\hat{P(k_1=k_2=...=k_{N}=k)}##(1) Homework Equations I also thought that the following imaginary exponential delta identity may be useful, due to the equality of...

If we have a series of, say, twenty coin tosses, then each discernable specific series of outcomes has equal probability to occur. However, there is only one discernable specific series consisting of twenty 1's, while there are many more discernable series consisting of ten 1's and ten 0's. So...

Or does ontological probability exist? I was reading an article that came up in my google searches ( https://breakingthefreewillillusion.com/ontic-probability-doesnt-exist/ ) ignore the free will philosophy stuff. But the author makes the claim that ontological probability simply does not...

Show that The standard deviation is zero if and only if X is a constant function,that is ,X(s) = k for every s belonging to S,or ,simply X=k. When they say constant function it means every element in S is been mapped to single element in the range.That is the single element is k. Which means...

How do we distinguish the decimal expansions of irrational numbers, and products thereof, from random sequences? Is an arbitrarily specified (not claimed to be perfectly randomly selected) numeric string, e.g. the 10^10th to 10^19th digits of the decimal extraction of the square root of 2.2...

Hi, I am trying to decrypt something in a .txt file as a challenge from a friend, the file contains: pÿd“ÙÃÊÌßéh'rv‹"^÷ù O˜w؉D•ÍúúYíY’ ∞¶iÀªÆzI¥r=«Å∑F¸¡„;≥ûü¸ã7∂.ˆ– ã<¿µD~’ÅsG›îwA_4Gå#›¥’6ª˝_ÎaÍÑjù]ÚU3Y{äF-Ê#i 33(›öR `?™|¸ ®flîè+zÂ√œ/fiãìR˛˙˚∂ZëìƺΩÒ†»˘∂®∑‘¬z vóR◊r∂Øûp)E...

Hi, Lets say I have N independent, not necessarily identical, random variable. I define a new random variable as $$Y=Σ^{N}_{i=0} X_{i}$$ does Y follow a normalized probability distribution?

Hello, I am looking at different methods for generating random numbers from the beta distribution. I am a bit confused about the following statement: "It is known that if ##a, b ∈ N_{>0} = \{1, 2, 3, . . .\}##, ##Y = \frac{\sum_{i=1}^a X_i}{\sum_{j=1}^{a+b}X_k}## is ##\mathrm{Be}(a...

Homework Statement In a given society, 15% of people have the sickness "Sa" , from them 20% have the sickness "Sb". And from those that don't have the sickness "Sa", 5% have the sickness "Sb" 1-We randomly choose a person. and we define: A:"the person having Sa" B:"the person having Sb"...

Homework Statement Let ##X_1 \sim N(3,2^2)## and ##X_2 \sim N(-8,5^2)## be independent. Let ##U=aX_1+bX_2##. What is the distribution of ##U## Homework EquationsThe Attempt at a Solution As they are independent, we can write the distribution of ##U## as the convolution of the 2. So I get...

I had a question regarding the random walk problem in statistical mechanics. If I drop, say, one molecule of KMnO4 in a beaker of water, what we generally observe (spread of KMnO4 to the ends of the beaker) is different from what we should get from probabilistic assumptions. I must be going...

Hi, I have this random variable ##\beta=\sum_{k=1}^K\alpha_k##, where ##\{\alpha_k\}_{k=1}^{K}## are i.i.d. random variables with CDF ##F_{\alpha}(\alpha)=1-\frac{1}{\alpha+1}## and PDF ##\frac{1}{(1+\alpha)^2}##. I want to find the CDF of the random variable ##\beta##. So, I used the Moment...

Hello guys, and sorry for my english in advance. I was presented some time ago with the following problem: Suppose there is a frog that jumps in any direction randomly, and all the jumps have size 1. What's the probability of, after 3 jumps, the frog be less than 1 unit from the origin. I...

In all Quantum Physics experiments, the sequence of measurement results is inherently random. Consider just the position observable. In the Schrodinger picture of non-relativistic QM, in each measurement-event, nature steps in and randomly selects one of the observable's eigenvalues/vectors to...

Homework Statement The same potato chip company reports that their bags of family sized chips each follows an approx. Normal distribution with a mean of 10.72 ounces and a standard deviation of 0.2 ounces. If the company wants to ship these chips into boxes that contain 6 bags, what would be...

I fill out receipt surveys a lot when there is a "big prize" ($1,000 usually...sometimes as low as $100 if I'm bored). Never won a drawing before. Has anyone else? Supposing one's primary reason for filling out these receipt surveys is to have a chance to win, is it mathematically just not...

We consider a monoatomic gas in a closed box. A textbook says : Since the assumption is that the particles move in random directions, the average value of velocity squared along each direction must be same. Why the assumption is that the particles move in random directions implies that the...

Hey! :o For a random variable $X$ the skewness is defined by \begin{equation*}\eta (X):=E\left (\left (\frac{X-\mu }{\sigma}\right )^3\right )\end{equation*} where $E(X)=\mu$ and $\text{Var}(X)=\sigma^2$. I want to show that \begin{equation*}\eta...

Is there a definition of "random(ness)"? Is it defined?

Homework Statement Given ##f_{X,Y}(x,y)=2e^{-x}e^{-y}\ ;\ 0<x<y\ ;\ y>0##, The following theorem given in my book (Larsen and Marx) doesn't appear to hold. Homework Equations Definition ##X## and ##Y## are independent if for every interval ##A## and ##B##, ##P(X\in A \land Y\in B) = P(X\in...

Homework Statement X is a Poisson Random Variable with rate of 1 per hour, following the Poisson arrival process a. Find the probability of no arrivals during a 10 hour interval b. Find the probability of X > 10 arrivals in 2 hours c. Find the average interarrival time. d. For an interval of 2...

Homework Statement X is a geometric random variable with p = 0.1. Find: ##a. F_X(5)## ##b. Pr(5 < X \leq 11)## ##c. Pr(X=7|5<X\leq11)## ##d. E(X|3<X\leq11)## ##e. E(X^2|3<X\leq11)## ##f. Var(X|3<X\leq11)##Homework EquationsThe Attempt at a Solution Can someone check my work and help me? a...

Chaos is deterministic behavior.Why is chaos deterministic.Why chaos is not random. Chaos is sensitive dependence on initial conditions,a slight change in initial condition can give rise to totally different trajectories.

Homework Statement See attached image (See below) Homework Equations Differential equations. And a combination of discrete & continuous distributions The Attempt at a Solution The Continous Distribution Function (CDF) is given in the question. So I differentiated it with respect to x...

Homework Statement Suppose a particle moves along the x-axis beginning at 0. It moves one integer step to the left or right with equal probability. What is the pdf of its position after four steps? 2. Homework Equations Binomial distribution ##P(k) = {{n}\choose{k}} p^k (1-p)^{n-k}## The...

Hello I have used a random number generator to create a list of uniformly random numbers, between 0 and 1. The usual check that I do is sorting the list, and histograming the difference between the following and the previous one. The shape of the histogram should follow an negative...

Post your drunk thoughts here (AKA, not thread worthy). Beer induced brain fart 1. When you microwave your dinner with clingfilm sealed over the top, the electrons in that air pocket get excited and the pocket expands (due to the air molecules moving faster right?). You get a clingfilm...

I'm trying to write a computer program which generates a random list of numbers but the random numbers form a bell curve, that is, there is a mean and a standard deviation from that mean. I'm not interested in some function that gets the job done, rather I'm trying to understand how do you...

From time to time I like to chat with flat Earthers and help them clear up their confusion. Today I came upon a question I couldn't answer, and since it is summer, I couldn't ask a professor. Would two people, on two separate planets, holding one pole, feel a push from the other...

Why nature has a lot of application of fibonacci sequence I mean why the number of spirals in the head of sunflower always has to be a memeber of fibonacci sequence, why pinecones displays similar patterns and many more examples. Do we really know the answer? I mean is this question is...

I've been experimenting with my own N-body simulation and I've found a seemingly unsolvable problem. When 2 particles cross paths exactly the peak velocity varies according to how close they are at their closest point and they either fly off the screen or slow right down, I can add an offset to...

Homework Statement Let 0≤p≤1. Let there be k distinct numbers (they can be natural numbers) a1, a2, ... , ak, each repeating respectively b1, b2, ... , bk times. Let q < ∑r=1k br Determine the minimal values of b1 ... bk such that the probability of q numbers chosen out of ∑r=1k br numbers...

Homework Statement I want to generate two random variables, one is normally distributed N ~N(10, 25) and the other one, E, is exponentially distributed with mean 1. I was not given a particular correlation coefficient.Homework Equations normal cdf, exponential cdf, inverse transform method...

Hello everybody. I have a Markowian homogeneous random walk. Given the transition matrix of the chain, I know that ##P[ X(t) = i | X(t-1) = j ] ≡ P_{j→i}=T_{ij}## where ##T## is the transition matrix and ##X(t)## is the position of the walker...

I want to create a plate of distinct circles on Matlab where their radii are generated by randn(1,p) and centers are random. I am currently doing the circles using viscircles, but some of them are overlapping, and since I want approximately 100 ones, this problem only gets worse. How can I make...

I am starting work on structural durability area for after treatment systems and deal with Random Vibration and PSD profiles quite often. However there are few fundamental questions about PSD profiles that I could not get answer to after a lot of search on internet. So finally decided to write...

Hi I'm trying to understand a paper that approximates the solution to Burger's equation (1D Navier Stokes) by a doing a one-dimensional cellular automaton simulation. I'm having a hard time understanding how all these topics connect. I have seen and walked through various demonstrations that...

Homework Statement Each day a quality engineer selects a random sample of 60 power supplies from the day's production, measures their output voltages, and computes a 90% confidence interval for the mean output voltage of all the power supplies manufactured that day. What is the probability...

Suppose we have two truly random sources A and B that generate bits ('0' or '1') synchronously. If we measure the correlation between the respective bits generated, we find a random, ie no, correlation. Now suppose A and B are two detectors that register polarization-entangled photons passing...

Here's a challenge of sorts, inspired by some previous discussions. You must choose a random number uniformly on the interval ##[0, 1]##. If the number is rational, someone wins a £1 million prize. If the number is irrational, no prize is won. It is your task to devise the method by which...

This work involves partitioning [ \, 0, 1 ] \, into an uncountable number of subsets, using choice to select a single element from each subset, and then defining a bijection from \mathbb{N} onto each subset using that selected element as a reference. The framework allows for proof of two...

Homework Statement [/B] https://www.physicsforums.com/attachments/screen-shot-2017-04-15-at-12-28-52-pm-png.194886/?temp_hash=4939cc24bd25e6adfbe75458bec6d011 Homework Equations [/B] P(X∈A,Y∈B)=P(X∈A)×P(Y∈B) The Attempt at a Solution If X and Y are independent then: P(X∈A,Y∈B)=P(X∈A)×P(Y∈B)...

I just have a couple of questions about how it can be zero probability. In case, you have a continuous cumulative probability distribution such that there is a derivative at each point not equal to zero. This means that every point as a different value than the other which means that every...