Probability Definition and 1000 Threads

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...

Homework Statement Homework EquationsThe Attempt at a Solution I can't understand the solution. Shouldn't the probability be 0.99^2 x (0.96^2 + 0.96(0.04) + 0.04^2) + (0.01 (0.99) +0.01^2) x (0.96^2). Please someone explain the solution to me

This was off-topic in the thread on vacuum fluctuations where the quote appeared, so I opened a new one. I didn't know the paper before, so first need to read it...

Homework Statement A train has got five train cars, each one with N seats. There are 150 passengers who randomly choose one of the cars. What is the probability that everyone will get a seat? I think that what is asking me is "what is the probability that each wagon is chosen by no more than...

Hey! :o At a gaming machine the probability of winning is 25%. A player plays 20 rounds. Which is the probability that he wins exactly five times? Which is the probability that in ten rounds he wins five times? Which is the probability that in ten rounds he wins ten times? Which is...

I have two questions about the use of stochastic differential equation and probability density function in physics, especially in statistical mechanics. a) I wonder if stochastic differential equation and PDF is an approximation to the actual random process or is it a law like Newton's second...

Two players, A and B, are playing a sequence of matches of some game. In each match, one player wins (there is no draw game in any match). For winning the match, the player gets 1 point, and for losing, 0 points. The match ends when one of the players first gets 6 points, and that player wins...

If the normalized probability density of the normal distribution is ## p(x) = \frac {1}{\sqrt{2\pi}\sigma} e^{-\frac{(x-\mu)^2}{2\sigma^2}} ##, then if ##\sigma = 0.0001## and in the special case ## x = \mu##, wouldn't the probability density at this point, ##p(\mu)##, exceed 1 since it is equal...

Homework Statement I have probabilty density ##\rho(\theta,\phi)=\frac{1}{4\pi} sin \theta d\theta d\phi## The question is let ##\theta## be measured with respect to the z-axis, find the probability ##p_{z}(z) dz ## that the particle lies between ##z## and ##z+dz##? Homework Equations see...

Homework Statement i'm having trouble coming up with an equation for this problem [/B] Mulder and Scully agree to meet at the FBI lobby sometime within a period of N minutes (e.g. 40 minutes). Each of them may show up anytime during that period (with a uniform distribution). If Scully arrives...

the probability of getting a head on flipping a biased coin is p. the coin is flipped n times producing a sequence containing m heads and (n-m) tails what is the probability of obtaining this sequence from n flips. i can't understand the wording

I am interested in your opinion with regards to expectation values of low likelihood events in QM. For example, Boltzmann brains are suggested as a problem in cosmology despite their probability being extremely miniscule. Is it realistic to expect Boltzmann brains and other low probability...

Sorry if this is trivial - I'm arguing with someone on Facebook :sorry: who is claiming that r-squared values, or correlation coefficients represents "chance" or "probability". I've never heard of this. I just need a simple yes or no answer along with a short explanation why it is or isn't...

What is the probability of having these 2 sets of numbers with 4 digits the same and 1 unique digit? Thank you. 12,547 11,425

Hello I'm trying to solve the following problem : a coin is tossed with probability 1/2 of giving head but if it lands head the probability of head rise to .9. If it gives tail again or if the number of head is bigger equal 5 in a row then it fails down to .5. I wrote a code running for...

Would you please introduce me some textbooks that offer multiple choice or true-false questions at the end of each chapter so I can practice before my final exam? Basically, that class I am taking right now cover many central topics in Undergraduate Probability course such as: • Moments and...

Homework Statement Let w(1) = event of a random walk with right drift (p > q, p+q = 1) starting at 1 returns to 0 Let p(w(1)) = probability of w(1) Let S=min{t>=0:wt(1)=0} be the minimum number of steps t a walk starting from 1 hits 0. What is E[S|w(1)]? Homework Equations I know E[S|w(0)] = 0...

Homework Statement On average, 2 students per hour come into the class. What is the probability that the time between two consecutive arrivals is in the interval <10 minutes; 50 minutes>. Homework Equations p(k)=P(Y=k)=((lambda*t)k*(e-lambda*t)/k! The Attempt at a Solution I've tried using...

Homework Statement You are playing a game with two bells. Bell A rings according to a homogeneous poisson process at a rate r per hour and Bell B rings once at a time T that is uniformly distributed from 0 to 1 hr (inclusive). You get $1 each time A rings and can quit anytime but if B rings...

i am trying to push myself and learn these furTher exercises in my maths i would any appreciate any comments and help. Question 1 what is probability u happens if n happens... P(U INTERSECTION N) / P(U)? Question 2 probability of U or S happening in the sample space of UDP or 52 byte size...

Please read this Insight here: https://www.physicsforums.com/insights/quantum-amplitudes-probabilities-epr/

Hello everyone, I'have implemented a Maximum-Likelihood-Expectation-Maximization Algorithm in order to reconstruct a bild. let say, we have such a system Ax=b, where A is a complex matrix, b is a complex vector. A and b are known and we will iterately try to find the best x (which should be...

Homework Statement An interaction occurs so that an instantaneous force acts on a particle imparting a momentum ## p_{0} = \hbar k_{0}## to the ground state SHO wave function. Find the probability that the system is still in its ground state. Homework Equations ##\psi _{0} =\left(...

Hi everyone, a colleague at work asked me a question this morning, which I answered with the caveat that I wasn't really sure. I would like to hear your opinion, please. His question was the following I have two different methods A and B to obtain a given desired outcome, and it's known that...

Homework Statement I need to use the overlap rule to find the probability that a measurement of a particle's energy at time t=0 will give the ground state E0 The normalized wave functions I have are...

Homework Statement A barbershop has two barbers: an experienced owner and an apprentice. The owner cuts hair at the rate of 4 customers/hour, while the apprentice can only do 2 customers/hour. The owner and the apprentice work simultaneously, however any new customer will always go first to the...

The question asks: A physical device can be in three states: A,B,C. The device operates as follows (all time units are in hours): The device spends an exponentially distributed amount of time in stateAA (with mean of 12minutes) and then with probability 0.6 goes to state B, and with...

So the problem asks: A computer server runs smoothly for Exp(0.2) days and then takes Exp(0.5)days to fix. The server is running fine on Monday morning, t=0. Find the probability that the server was fixed at least once (i.e. at least one complete repair was done) in the next 7 days and the...

I am having some difficulties in understand the convention of probability like P(A|E) ... And I am not able convert the questions into this for .I can solve those questions but can someone help me to understand this topic .And also multiplication theorem .

There is some confusion regarding notation of the arguments of a probability distribution. For example, MLE is defined as estimating the distrubution that gives the maximum probability of the observations x_i given the distribution parameters, p(x|\theta) . However my instructor stressed that...

Hi, I was wondering which course will be more beneficial to take first for a first year student majoring in computer science? Note: I tend to dislike proofs and theories. Discrete Structures - An introduction to the basic concepts of statistical analysis with special emphasis on engineering...

Why is the probability of finding a particle in an eigenstate of position zero and not one? When we say we have located a particle at a particular position - why is it always in a superposition of position eigenstates about that position. But still the probability should not be zero. I need...

Homework Statement A particle is in the n = 1 state of an infinite square well of size L. T. What is the probability to find the particle in the region Δx = 0.007L at the point x = L/2? 3L/4? (Since Δx is small you don't need to do any integration) Homework Equations ψ = Δxf(x) Δx = 0.007L...

Homework Statement . Suppose an electron is in the spin state (a,B) If sy is measured, what is the probability of the result h/2? Homework Equations Eigenvectors of the pauli matrix for y are (1,i)/Sqrt[2] (1,-i)/Sqrt[2] and if you are given a wave function of the sort a | +> +b |-> then the...

Homework Statement 1/ A committee of 6 is selected from 10 people, of whom A and B are two. How many committees can be form excluding A if B is included ? 2/ A committee of 5 is to be chosen from 6 boys and 4 girls. How many committees can be form containing a particular boy X but excludes a...

I'm reposting this piece of logic because my earlier attempts to get it across failed - nobody got what I was saying. This is about binary sequences like ##010110100111001001...##. All we need to know about a particular sequence is its length, ##N## and the number of 1's it contains. The logic...

Hi, I am a student in the Netherlands, and I'll be attending university next year. However, I am doing some form of research on Quantum Computing with another student for our so-called "profielwerkstuk" but my understanding of Quantum Physics and math is sometimes not at the level that is...

Homework Statement Consider a quantum mechanical system with three states. At each step a particular particle transitions from one state to a different state. Empirical data show that if the particle is in State 1, then it is 7 times more likely to go to State 2 at the next step than to State...

Hi, I'm struggling to understand probability coupling. I have the following problem: Let X and Y each be uniformly distributed on the discrete set {1,...6} (i.e. the distribution of the roll of 1 fair die). (a) If X and Y are independent, what is Pr[X = Y]? (b) Couple X and Y so that Pr[X = Y]...

In a certain lottery, you must select 6 numbers (in any order) out of 34 correctly to win. a.) How many ways can 6 numbers be chosen out of 34 numbers? b.) You purchase one lottery ticket. What is the probability of winning?

Homework Statement [/B] The question is phrased in the following way: There are 6 jobs to be assigned to 5 people. Each job is assigned only to one person, and each person must have at least one job. How many different arrangements are there? Homework Equations In general, I would approach a...

In another math thread https://www.physicsforums.com/threads/categorizing-math.889809/ several people expressed their opinion that, while statistics is a branch of applied mathematics, the probability theory is pure mathematics and a branch of analysis, or more precisely, a branch of measure...

Homework Statement ISW walls at 0 and L, wavefunction ψ(x) = { A for x<L/2; -A for x>L/2. Find the lowest possible energy and the probability to measure it? Homework Equations Schrodinger equation ψ(x)=(√2/L)*(sin(nπx/L) cn=√(2/a)∫sin(nπx/L)dx {0<x<a} En=n2π2ħ2/2ma2 The Attempt at a...