Probability Definition and 1000 Threads

Forgive me, I am not a probability guy, so I am unsure how well known this is. I was trying to figure something out and found this. I found it cool. Here's the explanation. The first solution is a fraction (damn scanner!) Oops! From Kendall Geometrical Probability (1963)

I've come up with a problem that's important for an algorithm I'm developing, and I don't know how to solve it. Wondering if anyone here can help? I have an initial set S1 of size N. S2 is created by randomly sampling M samples from S1 with replacement (meaning the same item could be selected...

The answer is ##4/7##. I know the denominator which is number of unconstrained outcomes is $$\dfrac{\dbinom{8}{2}\dbinom{6}{2}\dbinom{4}{2}}{4!}$$But I am not sure how to find the number of outcomes under the constraint. Could some give me a hint? Thanks.

Hi All, I want to ask how to calculate the absolute gamma probability from relative intensities ( found on the tables of nucliedes) following alpha or beta decay. I mean the probabilities that all add to 1. Many thanks.

Susskind explains how if you prepare an electron along any axis n (with an electromagnet) and then measure it along any other axis m, the probability of finding the electron with spin up or spin down is given by the angle between the axis. I have left out the linear algebra, because my question...

My questions: 1) What about if t = 2? Is there a certain meaning to ##G_X (2)## ? 2) PGF for uniform distribution is ##G_X (t)=\frac{t(1-t^n)}{n(1-t)}## and for t = 1 ##G_X (1)## is undefined so ##G_X (1) =1## is not true for all cases? Thanks

Let X denote the largest number shown on the four dice. P(X ≤ x) = (x/6)4 , for x = 1,2,3,4,5,6. Complete the following table: x 1 2 3 4 5 6 P(X=x) 1/1296 15/1296 65/1296 175/1296 369/1296 671/1296 The values in red are the answers, I don't understand how the answers were found. Thanks.

In a bag there are m white balls and n red balls with mn = 200 and there are more white balls than red balls. If two balls are taken randomly at once and the probability of taking two different colored balls is \frac{40}{87} then the value of 2m + 3n is ... A. 30 B. 45 C. 50 D. 70 E. 80 Okay...

Hey! An insurance office has $2500$ contracts with mean annual profit (per contract) $\mu=330$ and standard deviation $\sigma=540$. Calculate the probability that the total annual profit is not more than $800000$. I have one the following: The annual total profit should be not more than...

Hi hi, I was thinking about this, all of this starts playing a game, I'll show a simplification: We ca win several times. We have a count ##n##, where is the max number of rolls until you win, let's say we can win a ##m## amount. In every roll we can win ##m## with a probability of ##p##. If...

Given a probability density distribution ##P(\vec{x})##, for what named distributions is the following true: \begin{equation} \begin{split} P(\vec{x}) &= P_1(x_1) P_2(x_2) ... P_n(x_n) \end{split} \end{equation}

Today the youtube algorithm directed me to a video of someone playing geoguessr in the US until he got all of the 50 states at least once. If all states are equally likely this would take about 50*ln(50) tries. 50*(1+1/2+1/3+ ... 1/50), so about 200. Of course all states aren't equally...

Hi, Just a quick question about conditional and marginal probabilities notation. Question: What does ## p(a|b, c) ## mean? Does it mean: 1) The probability of A, given (B and C) - i.e. ## p[A | (B \cap C)] ## OR 2) The probability of (A given B) and C - i.e. ## p[(A | B) \cap C] ## I was...

Let $v$ and $w$ be distinct, randomly chosen roots of the equation $z^{1997}-1=0$. Find the probability that $\sqrt{2+\sqrt{3}}\le |v+w|$.

The image above is the problem and the image below is the solution I have tried but failed.

Hey! :giggle: One of the techniques we are using at the digital communications to improve the reliability of a noisy communication channel, is to repeat a symbol many times. For example, we can send each symbol $0$ or $1$ say three times. More precisely, applying the rule of majority, a $0$...

The wave function ψ(x) of a particle confined to 0 ≤ x ≤ L is given by ψ(x) = Ax, ψ(x) = 0 for x < 0 and x > L. When the wave function is normalized, the probability density at coordinate x has the value? (A) 2x/L^2. (B) 2x^2 / L^2. (C) 2x^2 /L^3. (D) 3x^2 / L^3. (E) 3x^3 / L^3 Ans : D

Summary:: Hello there, I'm a mechanical engineer pursuing my graduate degree and I'm taking a class on machine learning. Coding is a skill of mine, but statistics is not... anyway, I have a homework problem on Bernoulli and Bayesian probabilities. I believe I've done the first few parts...

Hi, I have a question about probability transformations when the transformation function is a many-to-one function over the defined domain. Question: How do we transform the variables when the transformation function is not a one-to-one function over the domain defined? If we have ## p(x) =...

Hi, I have question about finding marginal distributions from 2d marginal pdfs that lead to the probabilities being greater than 1. Question: If we have the joint probability distribution ## f(x, y) = k \text{ for} |x| \leq 0.5 , |y| \leq 0.5 ## and 0 otherwise. I have tried to define a square...

The probability that at least 2 of 3 people A, B, and C will survive for 10years is 247/315. The probability that A alone will survive for 10 years is 4/105 and the probability that C alone will die within 10 years is 2/21. Assuming that the events of t.he survival of A, Band C can be regarded...

When we apply creation operator in vacuum we certainly have one particle,similarly for annihilation operator.Then what is stand for chance(probability) in QFT?

Find the probability that this number is in set A but not in set B. (please see attachments) Is the answer to this simple maths secondary school homework 3/14. If not please help?

> 20 shoes, from 10 pairs of shoes, are lined randomly. What is the > probability that there is a set of 10 consecutive shoes with 5 left shoes > and 5 right shoes? I thought that would be a good idea to imagine 10 shoes as one unique object, as follow: Instead enumerate 20 objects, let's...

Hi, I have a quick question about something which I have read regarding the use of dirac delta functions to represent conditional pdfs. I have heard the word 'mask' thrown around, but I am not sure whether that is related or not. The source I am reading from states: p(x) = \lim_{\sigma \to...

Hi, I'm new to PF and not really sure which forum may be the most appropriate to find people with an interest in probability and entropy. But the title of this forum looks promising. If you share an interest in this topic would be delighted to hear from you.

Thinking of the common language notion of "entropy" as "uncertainty", how can running a simulation based on a probability model implement entropy increasing? After all, the simulation picks definite outcomes to happen, so (intuitively) there is less uncertainty about the future as definite...

Given we only have one number I assume we are to use Poisson distribution. Probability for a plane with two engines to fail require both engines to fail: $$P_2 = P_o(2) =p^2/{2!} * e^{-p}$$ Probability of a four engine plane to fail requires 3 or 4 engines to fail: $$P_4 = P_o(3) + P_o(4) =...

this is a textbook problem shared on a whattsap group by a colleague... i have no problem in finding the value of ##k=0.08##, i have a problem with part (ii) of the problem. I have attached the solution here; how did they arrive at the probability distribution of ##y##? attached below is...

I don't intend to sound macabre, but I was having this thought if I have to quantify the probability of someone dying given his age (in days) how would I go about quantifying that with a minimal accuracy (ok if it's not accurate but I just need some number with days). Has anyone ever worked out...

I only know that if E>V, then the frequency would be higher where E-V is higher. But what does that have anything to do with probability?

I don't understand why ? ## \Psi ∇ ⋅ (A \Psi^ *) + \Psi ^* ∇ ⋅ (A \Psi ) = 2 ∇ ⋅(A \Psi ^* \Psi) ## form ## ∇ ⋅ (fg) = ∇f ⋅ g + f(∇ ⋅ g) ## Attempt at a Solution ## \Psi ∇ ⋅ (A \Psi^ *) + \Psi ^* ∇ ⋅ (A \Psi ) = 2 ∇ ⋅ (A \Psi ^* \Psi) - ∇\Psi ^* ⋅ A\Psi - ∇\Psi ⋅ (A\Psi ^*) ##

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The summary says it all: why is the probability of an event not calculated by the probability that it is the event AND that it is not any other? Sounds silly, and I am certain the explanation is simple, but I don't see it.

Suppose that W(t) is just a Wiener process (i.e. a Gaussian in general). I want to know what the probability density for x, P(x), is. I started off by just assuming that I want to measure the expectation value of an observable f(x), so ##<f(x)>=\int_{W=0}^{W=t}{P(W)f(g(W))dW} \ \ ,\ \ x=g(W) ##...

First of all, I've calculated the partition function:Z=1h3∫e−βH(q,p)d3pd3q=1h3∫e−β(p22m−12mrω2)d3prdrdθdz=2πL(2mπh2β)3/2e12βmω2R2−1ω2mβThe probability of being of one particle in radius $r_0$ is: p(r=r0)=1Z∫e−βHd3pd3q=∫1Z2πL(2mπh2β)3/2eβmrω22rdr So I've thought that because, by definition, the...

Kindly assist with these questions: Data showed that 22% of people in a small town was infected with the COVID-19 virus. A random sample of six residents from this town was selected. 1) What is the probability that exactly two of these residents was infected? 2) What is the probability that at...

Let's say you have a leaking tab, and the probability of a droplet in any given second is 1%, regardless of whether there was a drop previously. How would you calculate the probability of n drops in a minute? No drops in a second is 0.99, so no drops over a minute is 0.99^60. Hence one or more...

Suppose we have an operator with three eigenvectors/eigenvalues ##e_1##, ##e_2## and ##e_3##. The operator measures wavefunction ##\psi##. Could we say that we find outcome ##e_x## with probability ##P(\psi,e_x)##, and could we extend this to an infinite dimensional operator as a spectrum of...

Given a particle in a 1D box with a finite number of states ##m##, is the probability a particle is in a certain state ##n## equal to the energy of that state divided by the sum of energies of all states? In other words, given $$ E_n = \dfrac{n^{2}h^{2}}{8mL^{2}}$$ is $$P_n=...

My approach to this problem is a little laborious, it involves three coordinates, probably it is right, but tiring and extensive beyond what the question wanted. Be the origin in the rectangle middle. It would be like: imagine a rectangle with opposite sides L and R with length l, so to find...

In ##\mathbb{R}^2##, there are two lines passing through the origin that are perpendicular to each other. The orientation of one of the lines with respect to ##x##-axis is ##\psi \in [0, \pi]##, where ##\psi## is uniformly distributed in ##[0, \pi]##. Also, there are two vectors in...

I want to find the probability that the two points ($x_1, y_1$) and ($x_2, y_2$) lie on the opposite sides of a line passing through the origin $o = (0, 0)$ and makes an angle $\psi$ that is uniformly distributed in $ [0, \pi]$ with the $x$ axis when the angle is measured in clockwise direction...

I have been looking for a way to learn probability and statistics online and have searched but found nothing yet. I am looking for a course on probability and statistics that will not only teach me the basics but all there is to know about the subject. I would love it if the visualizations are...

Hello, everyone. The projection postulate says the wave-function collapses to one of its eigenstates under measurement, does it talk about each probability with which the wave-function collapses to those possible eigenstates?

Starting with finding the probability of getting one of the states will make finding the other trivial, as the sum of their probabilities would be 1. Some confusion came because I never represented the states ##|\pm \textbf{z}\rangle## as a superposition of other states, but I guess you would...

"Prove Theorem 7.1 about the probability of a union, using the 12.3 proof (see section 12.2) that involves indicator variables. Do not write the proof in full generality, only for three events. You should not use the product notation; you should write out all factors of the product." I'm taking...

Hi PF, A(x,t) is the probability amplitude at time t that a particle is at x. If it was emitted at (0,0) the propagator gives its value. I wonder if QM can give the amplitude of time probability B(y,t) that an impact will occur (for a given y) at any t. consider a screen behind the two slits, it...

1) Since I want at least ##6## flights to come within ##2## hours, then the time interval between each should be, at worse, ##2/6=1/3## hours, and the probability is ##P(X\leq1/3)=1-e^{-1/3}##. 2) The probability that at best 5 airplanes arrive at the airport is...

Suppose P(B|A)=1. Does that mean that P(A|B)=1?