Probability Definition and 1000 Threads

Homework Statement Presume the relation ##\frac{x}{x+y^2}-y=x## is defined over the domain ##[0,1]##. (a) Rearrange this relation for ##y## and define it as a function, ##f(x)##. (b) Function ##f(x)## is dilated by a factor of ##a## from the y-axis, transforming it into a probability density...

Su, Francis, et. al. have a short description of the paradox here: https://www.math.hmc.edu/funfacts/ffiles/20001.6-8.shtmlI used that link because it concisely sets forth the paradox both in the basic setting but also given the version where the two envelopes contain ( \,\$2^k, \$2^{k+1}) \...

Homework Statement Hello all, I created a predictive model from a data set of observed values and am looking for probabilities for accuracy. Data set A (observed) and data set B (predictive model) have a correlation of 84 % using linear regression. Data set A and B are both normally...

Hi all, I am thinking a problem of drawing a ball in a sealed box. Assuming there is a box, contains plenty red and white balls, the number of red and white balls are unknown but let's assume there will be ##p## chance to draw a red ball and ##q=1-p## chance to get a white one. Those...

What I know: A ripple/wave in a field gives rise to a particle. For example, a ripple in electric field creates a photon. Question: Is this the same principle as probability wave which when observed reveals a particle?

Homework Statement The wave function of a particle of mass m confined in an infinite one-dimensional square well of width L = 0.23 nm, is: ψ(x) = (2/L)1/2 sin(3πx/L) for 0 < x < L ψ(x) = 0 everywhere else. The energy of the particle in this state is E = 63.974 eV. 1) What is the rest energy...

Homework Statement Homework Equations $$f_X(x)=\lambda e^{-\lambda x}$$ $$F_X(x) = 1-e^{-\lambda x}$$ $$\mu = \frac{1}{\lambda}$$ The Attempt at a Solution a) $$f_{X,Y}(x,y) = f_X(x)f_Y(y) = \frac{1}{800} e^{-\frac{1}{800}x} \frac{1}{1000}e^{-\frac{1}{1000}y}$$...

I’m currently evaluating the "realism" of two survival models in R by comparing the respective Kullback-Leibler divergence between their simulated survival time dataset (`dat.s1` and `dat.s2`) and a “true”, observed survival time dataset (`dat.obs`). Initially, directed KLD functions show that...

A question came up to my mind while thinking about probabilities and Born rule in the context of the Everettian approach. It is often said that anomalies/maverick branches where the experiments go horribly wrong and crazy stuff happens have a negligible amplitude/measure so they really don't...

Homework Statement From various studies, it is known that once an individual is infected with a virus, they become infectious at rate λ. The individual will recover at rate λ, independent of the time it took for them to become infectious. Let X be the total amount of time an individual has this...

Given this libreoffice command: HYPGEOM.DIST(X; NSample; Successes; NPopulation; Cumulative) >X is the number of results achieved in the random sample. >NSample is the size of the random sample. >Successes is the number of possible results in the total population. >NPopulation is the size...

Hi, I am trying to write a function which would take two arguments: -> number of bits (which are a binary 0 or 1 value) N -> and acceptable number of mismatching bits M The function would statistically determine the probability of having M or less mismatching bits when randomly generating two N...

Given this base data (taken from Graphical Models )$P(C) = 0.5$ $P(\lnot C) = 0.5$ $P(R | C) = 0.8$ $P(R | \lnot C) = 0.2$ $P(\lnot R | C) = 0.2$ $P(\lnot R | \lnot C) = 0.8$ $P(S | C) = 0.1$ $P(S | \lnot C) = 0.5$ $P( \lnot S | \lnot C) = 0.5$ $P( \lnot S | C) = 0.9$ $P(W | \lnot S, \lnot...

Restricting to finite dimensional QP, suppose a system is in a state S1, an experiment is done, and state S2 is one of the eigenstates (assume all eigenvalues are distinct). The probability that the system transitions from S1 to S2 is p = Trace( S1*S2), using state operator notation. On the...

Dear All sorry for repeated post; There is a problem Problem: Three cards are drawn in succession from a deck without replacement. find the probability distribution for the number of spades. I have come with this solution. Let S1: appearance of spade on first draw S2: appearance of spade on 2nd...

Dear all Please help in solving the following problem. A large industrial firm uses 3 local motels to provide overnight accommodations for its clients. from past experience, it is known that 20% of the clients are assigned rooms at the Ramada Inn, 50% at the sheeraton and 30% at the Lakeview...

This ought to be some simple gap in my knowledge, but it bugs me nonetheless. Let me present the argument as I see it, I'm fairly certain that there is just some tiny part that I didn't learn correctly. Let us assume a wavefunction $$\Psi$$ is defined as a superposition of two wavefunctions...

So, at a car rental company, 20% of car reservations are not claimed. There is a total of 22 cars and the manager takes 25 reservations a day. If all cars are claimed for a day, what is the probability that one or more customer who had reservations were unable to claim their car? I need to...

Homework Statement ##\displaystyle \int_{- \infty}^{\infty} \frac{1}{\sqrt{2 \pi}} x e^{- \frac{x^2}{2}} dx## Homework EquationsThe Attempt at a Solution So first off, obviously the answer is 0, because the integrand is odd and we have symmetrical limits of integration. However, when I make...

As far as we know, the universe is undergoing accelerated expansion and heading towards empty de Sitter space. It is assumed that eventually the observable universe will be emptied out of matter and all radiation. Now if we take in account quantum mechanics, there's always non zero probability...

Homework Statement [/B] Driving to work, a commuter passes through a sequence of three traffic lights. At each light he either stops, denoted by s, or continues, denoted by c. Assume that the outcome c or s for each traffic light is independent of the outcome of other traffic lights. (a)...

The conservation of probability says: $$\partial_t J^{0} + \partial{i}J^{i} = 0$$ Use the Schrodinger equation to obtain$$ J^{i} (\vec r)$$. I have no idea where to start this kind of problem because the notation makes no sense to me. I would appreciate a hint or nudge in the correct direction.

I had taken probability before but not in depth and I want to learn it again. Is David Morin's book good for a intermediate learner ? I don't want to waste time on easy stuff. The reviews are good but popular science books tend to omit proofs instead they just state the theorems and have easy...

I'm considering taking the upper-level probability course at my school over the elementary course offered because of time constraints. The latter is not a prerequisite for the former. Do you think I will be alright taking the more advanced probability course over the elementary course? Any input...

The colloquial statistical mechanics explanation of entropy as if it is caused by probability is dissatisfying to me, in part because it allows highly organized (i.e. with a real potential for work) arrangements to appear as 'random fluctuations', though with very low probability. But as far as...

I really need help on how to solve this (Sweating): A dice game involves rolling 2 dice. If you roll a 2, 3 , 4, 10, 11 or a 12, you win \$5. If you roll a 5, 6, 7, 8, or 9, you lose \$5. Find the expected value you win (or lose) per game.

Hey there! So the problem is like this: We choose 10 random cards from a normal deck of cards(52 cards). What is the probability that we get: a. 0 aces b. maximum 3 aces c. at least 1 ace and at least one face card I'm unsure which formula I should use. I have thought that maybe the sample...

Homework Statement Two components of a laptop computer have the following joint probability density function for their useful lifetimes X and Y (in years): f(xy)=xe^(−x(1+y)) 0 <= x <= y 0 otherwise Find the marginal probability density function of X, fX(x). Enter a formula below. Use * for...

Homework Statement [/B] There are six pairs of cups and saucers; two are red, two are white and two blue. 1. Ignoring the saucers, calculate the number of distinct arrangements of the cups. 2.Determine the number of distinct arrangements such that no cup is on a saucer of the same pattern for...

Homework Statement Homework Equations I solve the (a) , using even,odd function. So, C=1/a The Attempt at a Solution I don't know how to approach (b). I think that 'total energy of the system' doesn't mean expectation value, how can i get total energy and probability of them?

TL;DR: My professor asked me to graph the probability that a particle would be excited from the ground state to a stationary state with a certain energy E (y-axis) verse the energy of that new state (x-axis). I need help finding this probability as a function of E. Probability=|<ΨE|P|Ψg>|2 P is...

Consider the double slit experiment; if we position a detector at, say, the left slit, will a single particle, say, an electron, when fired at the slits, always be detected at the left slit, or will it be detected at the left slit 50% of the time? (so that it is 50% of the time at the right slit)

Homework Statement I post here to check if I am in the right way to understand this point in the book. The wave function of free particle is ##Ae^{\frac{i}{\hbar}(px-Et)}##.This could be regarded as ##{\phi}(x,t)=Ae^{\frac{i}{\hbar}S(x,t)}##. ##S(x,t)## is the free particle's least action...

1. Homework Statement if δ=7.7 %; Pm=0.2349 and if δ=30.8 %; Pm=0.9180. 2. Homework Equations The Attempt at a Solution We can calculate value of c if we know value of Pm and δ? Please help me. Thanks You![/B]

Homework Statement This excresice is supposed to help you understand the basic operations of sets, later used in probability. I am given the following phrases and have to write them in using mathematics. Given three events A, B and C, which belong to sample space S, calculate the following...

Suppose we have a "particle" which can be at some position x∈N (where N={0,1,2,...}). The probability that the particle is at position x can be written as: P(x) = 1/(2x+1) Now suppose we have two particles p1 and p2.To keep things simple, assume that the individual probability distribution for...

Homework Statement Each week, Stéphane needs to prepare 4 exercises for the following week's homework assignment. The number of problems he creates in a week follows a Poisson distribution with mean 6.9. a. What is the probability that Stéphane manages to create enough exercises for the...

Homework Statement I want to plot a graph of the survival probability of the initial state ψ = e-|x| for a free particle. Hopefully this will enable me to plot some more difficult examples like the inverted oscillator etc for a project but I'm struggling fundamentally with the free particle...

I'm pretty new to quantum, so I'm pretty sure I'm missing something basic here. I've got a 4x4 Hamiltonian with eigenkets $$\psi_{U} = 1/(\sqrt 2) (\psi_{1up} \pm \psi_{2up})$$ and $$\psi_{D} = 1/(\sqrt 2) (\psi_{1down} \pm \psi_{2down})$$ The only difference between the two states is the spin...

Problem: I'm interested in studying the probability of an event involving a random vector. Specifically, I'm interested in (∂/∂a)Pr[X>( (Y-a)/Z )] Where "a" is a non-random parameter and the random vector {X,Y,Z} is distributed Normal( µ, Σ) for µ={0,0,0} and Σ= {{1, 0.5, 0.5}, {0.5, 1, 0}...

I am a laymen of sorts in both physics and philosophy. I embarked on a trip to acquaint myself (gently at first) with contemporary physics. My question is foundational and therefore probably philosophical. If it is off-topic, please kindly point me to any place where such discussions may be...

Homework Statement I look at the distribution ##(Y_1,Y_2,...,Y_n)## where ##Y_i=μ+(1+φ x_i)+ε_i## where ##-1<φ<1## and ##-1<x_i<1## . x's are known numbers. ε's are independent and normally distributed with mean 0 and variance 1. I need to find the the maximum likelihood estimator for μ and...

Homework Statement In a company, out of a sample of 20 bulbs, the mean number of defective bulbs are 2. Out of 1000 such samples, how many samples would have atleast 3 defective bulbs? Homework Equations Mean = n * p where n is number of bulbs and p is probability of a bulb being defective...

Homework Statement Q6. A function, ##f\left(x\right)=\frac{ax+1}{\left(ax-1\right)^3-\frac{a}{\left(x-1\right)^2-1}}##, can be defined as a PDf over the domain ##(0, 2)##. Express answers to 4 decimal places unless specified otherwise; (a) Find the value of ##a## given that ##f(x)## is a PDf...

Homework Statement Does anyone know of a simple proof for this: https://s30.postimg.org/tw9cjym9t/expect.png E(X) = E(X|S)P(S) + E(X|S_c)P(S_c) X is a random variable, S is an a scenario that affects the likelihood of X. So P(S) is the probability of the scenario occurring and and P(S_c) is...

This is a rather basic question but I seem to be stuck, given a system made up of two subsystems how do I compute the probability of subsystem B to be in some state (for example I've got |p>=|a>|b> if I measure the second part what's the probability of it being found in state |c>, how am I...

Homework Statement Find the average energy ##\langle E \rangle## for (a) an n-state system in which a given state can have energy 0, ε, 2ε, 3ε... nε. (b) a harmonic oscillator, in which a state can have energy 0, ε, 2ε, 3ε... (i.e. with no upper limit). Homework Equations Definition of...

Hello and I would like to thank you for your space in this website I'm from Greece and i have exams in next days I need some help with an exercise that I can not solve! There is a probability density function with the following type : P(Y=y/X=x)=f(y,x)= $${n \choose y}* {x}^{y} *...

Hello and i need your help with the following statistic ploblem! in a party there are n people (n >=2). each man cast identity in a common box.They mix and each person chooses identification at random from the box, without resetting. We say that we have success if one chooses his identity. If...

Hi ! I'm not sure to post my question in the right place so I'm sorry if I'm wrong...! I have a particle associated with a certain spectrum in energy S (differential cross section). When the particle interacts I use this distribution to have the energy lost. Now, if my particle interacts 2...