Probabilities Definition and 398 Threads

Suppose we have two series of independent Bernoulli experiments with unknown probabilities ##p_1## and ##p_2##. The first series registers ##x_1## successes in ##n_1## trials while the second series registers ##x_2## successes in ##n_2## trials. Is there a way that we can compute probability...

Homework Statement Homework Equations The Attempt at a Solution The first part I'm not worried about, but the second part is worked out in the "relevant equations" section. Honestly, it looks like more magic than a Harry Potter movie going on there to me. I'm at a loss as to what...

Homework Statement Selecting Two Balls. Suppose that two balls are to be selected at random, without replacement, from a box containing r red balls and b blue balls. We shall determine the probability p that the first ball will be red and the second ball will be blue I am confusing Pr(A|B) and...

Hello, I am a student in the Actuarial bachelor's degree. I've just finished my Stats and Probabilities class in which we completed the Introduction to Probability book by Ross. I really enjoyed this class and would like to continue studying this branch can you suggest a book that continues...

I started to study statistical physics from a book, and it starts with basics about statistics and probabilities (which are things mostly new for me). In the book there is the following statement: "The simplest non-trivial system which we can investigate using probability theory is one for...

Could somebody please tell me, in layman's terms, the answer to the following: When 7 standard six sided dice are thrown what are the odds of 4 showing the same number, 5 showing the same number, 6 and 7. Also the odds of 7 sixes being thrown. This is all to do with a game used to raise money...

I have been following a series of Leonard Susskind's lectures called 'Quantum Entanglements' (Part 1). In general, he explains how to find the probabilities of measurements of spin ½ particles' states, both single particles and pairs of them. I have learned the following: how to use the 2x2 spin...

I am looking into the probability for : \mathcal{P}(B^0 \rightarrow B^0). I said that if I start from a state |B^0> = \frac{1}{\sqrt{2}} (|B_L> +|B_H>) with L(ight)/H(heavy) are the mass eigenstates, then after some time t the state will evolve: |B^0(t) > = e^{-iHt} |B^0>= \frac{1}{\sqrt{2}} (...

Hi, I calculated the probability to this scenario: getting between 3 and 6 Heads after tossing a coin for n=10 trials... The binomial probability for this is: P(3 \le k \le 6) = \sum_{k=3}^6 Bi(k;p,n)= \sum_{k=3}^6 \frac{n!}{k!(n-k)!} p^k (1-p)^{n-k} =\sum_{k=3}^6 \frac{10!}{k!(10-k)!}...

Homework Statement Homework Equations The Attempt at a Solution For a angular momentum ##J##, there exists the eigenvalue problems $$J^{2} \mid j \hspace{0.02 in} m \rangle = j(j +1)\hbar^{2} \mid j \hspace{0.02 in} m \rangle $$ $$ J_{z} \mid j \hspace{0.02 in} m \rangle = m \hbar \mid j...

Let's assume we're living in a mechanical deterministic world. Now do you agree that any uncertainty is a result of lack of knowledge? We flip a symmetric coin. The equations of movement are deterministic, but the outcome is uncertain, with probability 50% tail or head. Thus, it's the initial...

Hi All, First, the context for this question can be found in Wilde's Quantum Shannon Theory text on the arXiv, specifically the section starting at the bottom of page 98, entitled "Entanglement in the CHSH Game". My particular question relates to Exercise 3.5.11 on page 100 of the same...

Hello, I am stuck at this exercise: 1. Homework Statement X ~ U(0, a), a > 0 and Y = min(X; a=2). - Find the cumulative distribution function of Y -Is the variable Y continuous ? Homework Equations 3. The Attempt at a Solution [/B] The density function for X is f(t)= 1/a if 0≤t≤a , 0...

If two 5-year survival probabilities are p1=.55 and p2=.41 the ratio is .55/.41 = 1.34 but since probabilities are in [0, 1] should I take the log first? Which is the more appropriate way to interpret the ratio? the ratio of logs is Log(.55)/log(.41) = .671 Which is less than one although...

Hey everyone. Question! If the probability of A is .3 and the probability of B is .8, can A and. B be mutually exclusive? This is confusing me!

Homework Statement Problem(s): Suppose that X has an exponential distribution with mean equal to 10. Determine the following: (a) P(X > 10) (b) P(X > 20) (c) P(X < 30) (d) Find the value of x such that P(X < x) = 0.95. Correct answers: (a) 0.3679 (b) 0.1353 (c) 0.9502 (d) 29.96 Homework...

Hello 1. Homework Statement Consider fk N*→N, k≥0 fk(n)=Σ jk n>0 We're looking to establish these identities, using a combinatorial argument fk(n)=n if k=0 fk(n)= 1/(k+1) [ nk+1 + Σ ( i , k+1) (-1)k+1-ifi(n) ] if k>0 the sum is about i from i=0 to i=k-1 and (i, k+1) is the combination...

Let's consider a simple roulette game, where one may either get red or black. Since the probabiblity P of an event A, P(A) is defined as the relative frequency at which the event occurs, if we get red , say 3 times in a row, it is very likely that the next random pick will be black. My question...

Homework Statement -A bus is moving along an infinite route and has stops at n = 0, 1, 2, 3, ... -The bus can hold up to B people -The number of people waiting at stop n, Yn, is distributed Poisson(10) and is independent from the number waiting at all the other stops. -At any given stop each...

Homework Statement PROBLEM(S): A computer system uses passwords that contain exactly eight characters, and each character is one of 26 lowercase letters (a–z) or 26 uppercase letters (A–Z) or 10 integers (0–9). Let Ω denote the set of all possible passwords, and let A and B denote the events...

Suppose i have an experiment which can give result 0,4 but that the probability p(4)<=1/sqrt(2). Does this make sense in a frequentist approach since if i do the real experiment once and got 4 then the probability (statistics a posteriori) for 4 is 1 which is a dumb counterexample.

Homework Statement In a spin-\frac{1}{2} system all particles are in the state |\psi\rangle. 3 experiments performed and are separate, the results are as follows: Particle in state |\psi\rangle, measured S_z = \frac{\hbar}{2}, with P=1/4 Particle in state |\psi\rangle, measured S_x =...

Homework Statement A particle is in the ground state of a L-box. At t = 0 the wall at x = L is suddenly moved to 2L. (a) If an energy measurement is made after the wall is moved, what is the probability of measuring the energy to be that of the ground state of the new box? (given solution...

Homework Statement Among a large group of patients recovering from shoulder injuries, it is found that 22% visit both a physical therapist and a chiropractor, whereas 12% visit neither of these. The probability that a patient visits a chiropractor exceeds by 0.14 the probability that a patient...

Homework Statement The e-functions for n=0,1,2 e-energies are given as psi_0 = 1/(pi^1/4 * x0^1/2)*e^(x^2/(2*x0^2) psi_1 =... psi_2 =... The factor x0 is instantaneously changed to y= x0/2. This means the initial wavefunction does not change. Find the expansions coefficients of the...

I've been thinking about the Central Limit Theorem and by my understanding it states that the sum of randomly distributed variables follows approximately a normal distribution. My question is if you have, say, 100 uniformly distributed variables that range from 0 to 10, their sum has to be...

This is a question about The Computational Capacity of the Universe by Seth Lloyd. It seems to me that arbitrary real numbers cannot be part of the state of the universe, since they carry an infinite amount of information. There are transition probabilities from the current state of the...

Homework Statement An operator \mathbf{A}, corresponding to a physical quantity \alpha , has two normalized eigenfunctions \psi_1(x)\quad \text{and}\quad \psi_2(x), with eigenvalues a_1 \quad\text{and}\quad a_2. An operator \mathbf{B}, corresponding to another physical quantity \beta, has...

Homework Statement A Markov process with 4 states evolves in unit time steps with a transition probability matrix given by P = |0.5 0 0.3 0.2| |0.1 0.4 0.2 0.3| | 0 0.4 0.4 0.2| |0.1 0.1 0.1 0.7| Find the equilibrium probabilities for this system. What is the most likely state...

If we consider a bipartite system as in EPRB experiment we get the probabilities : p(++)=p(--)=1/4*(1-cos(theta)) p(+-)=p(-+)=1/4*(1+cos(theta)) p(+A)=p(+B)=p(-A)=p(-B)=1/2 Thus the sum of all the probabilities equals 3... How does that come ? Is it because in fact there are only...

So I am working with a Hidden Markov Model with continuous observation, and something has been bothering me that I am hoping someone might be able to address. Going from a discrete-observation HMM to continuous-observation HMM is actually quite straightforward (for example see Rabiner's 1989...

Hi All, Would it be reasonable to state that, together with the quantum mechanics appearance, there appeared also a new way to calculate probabilities? I have never heard any teacher pointing out that QM has brought a new probability method. They speak of amplitudes of probability but...

i got the answer to the following problem wrong: "there are four children in in the family. what is the probability that there are three girls, given that the youngest child is female?" my (updated) answer: the youngest is female, so three out of two children must be female. there are three...

Imagine some kind of system, where you have at t=0 N single atoms (a gas). Now in a later instant dt there is a certain probability that 2 atoms will have collided and formed a 2-atom unit. Similarly dt after this event there is a certain probability that this 2-atom unit has either collided...

Homework Statement The problem is a series of problems all relating to each other. I have gotten most of this done but I will add my answers and continue until the last part which is my main question: We choose a magnetic field in the z direction. Use your knowledge of 2-dimensional...

The Bureau of the Census reports that the median family income for all families in the United States during the year $1991$ was $\$35,353$. That is, half of all American families had incomes exceeding this amount and half had incomes equal to or below this amount (Wright 1992, p. 242). Suppose...

Homework Statement Suppose the angular wavefunction is ##\propto (\sqrt{2} cos(\theta) + sin (\theta) e^{-i\phi} - sin (\theta) e^{i\phi})##, find possible results of measurement of: (a) ##\hat {L^2}## (b)##\hat {L_z}## and their respective probabilities. Homework Equations...

Hey,I am making an app that counts probabilities in c++(win32){for those who knows}. I have found three formulas of equation,but I need some help for one. For example we have a die,and we hit it 6 times. Can we count with an formula,the probabilities to have the number "5",three times...

For a long time now I've been thinking about something I find odd about probabilities. For example, let's say that I win the lottery, something that is extremely unlikely. What is the probability that I will be struck by lightning? The odds of someone winning the lottery and getting struck by...

Let $(\Omega,\mathcal F,P)$ be a space of probabilities and $(A_n)_n\subseteq \mathcal F.$ Show that a) if the sequence satisfies $\inf\{P(A_n)_n:n\ge1\}=\alpha,$ with $\alpha\ge0,$ then $P\left( \bigcap\limits_{n=1}^{\infty }{\bigcup\limits_{k=n}^{\infty }{{{A}_{k}}}} \right)\ge \alpha .$ b)...

Hi all, could somebody look over my answer please. I'm pulled the equation I used off the internet but can't remember where so I'm not sure what it's called. I took a picture of my answer as I thought it would be easier to read than fiddling with symbols here. QUESTION ANSWER ATTEMPT...

Hi, I think I read here; maybe not, that , within a non-standard model of the Reals, it is possible to have probabilities , say over an interval, so that each point has non-zero probability. AFAIK, the transfer principle ( a.k.a elementary equivalence of models) does not disallow having a...

Homework Statement Let X(t) and Y(t) be independent Poisson processes, both with rates. Define Z(t)=X(t)+Y(t). Find E[X(1)|Z(2)=2]. 2. The attempt at a solution...

After a few months off (yay summer/internships), I'm 'back in the saddle' and I'm trying to catch up with my Q-mech. I have a wave function which is given as a particle sliding freely on a circular wire: \Psi = A(1 + 4cos\phi) I need to find the corresponding probabilities. So I know that I...

Homework Statement This isn't really homework, just reviewing for a test. This is problem 3.17 in 'A modern introduction to probability and statistics: understanding why and how' Dekking. But since it can be seen as a HW problem, might as well post here. Question: You and I play a...

Let's say we are doing interference experiment via say a Mach-Zehnder http://en.wikipedia.org/wiki/Mach%E2%80%93Zehnder_interferometer In the Mach-Zehnder two of the mirrors are half silvered. The photon has a 50% chance of passing through the half-silvered mirror and 50% chance of...

Homework Statement You are a real estate salesperson and you currently have 10 listings. Past experience has shown that you will sell approximately 70% of your listings. If sales are independent: What is the probability that you make exactly 8 sales? Homework Equations The Attempt...

Homework Statement Given the function F(x) = 1 - e^(-ax) - axe^(-ax) for x>=0 and 0 elsewhere, for which values of 'a' does the function constitute a CDF? Homework Equations The Attempt at a Solution I started with saying for that to occur, provided x1>x2 -> F(x1) > F(x2)...

Let's say we have a very simple game of two-card poker, where the deck consists of only 4 aces and 4 kings. There are 28 possible combinations: Six pairs of aces, six pairs of kings, and 16 ace-king hands. In play against a single opponent, both players are dealt two cards, face down. The...

Finding probabilities through general addition rule Homework Statement http://postimg.org/image/q9ztktpot/ Homework Equations P(A or B)=P(A)+P(B)-P(A and B) P(A and B)=P(A)P(B)The Attempt at a Solution The question is for part b). It said it was only focused on the mens so i ignored all the...