Probability distribution Definition and 203 Threads

Probability Question About "The Poisson Probability Distribution" Homework Statement - Assume that 1 in 200 people carry the defective gene that causes inherited colon cancer. A sample of 1000 individuals is taken. Use the Poisson approximation to calculate the appoximate standard deviation...

Homework Statement Suppose that .10% of all computers of a certain type experience CPU failure during the warranty period. Consider a sample of 10,000 computers. a.)What are the expected value and standard deviation of the number of computers in the sample that have the defect? b.) What...

Homework Statement The College Board reports that 2% of the 2 million high school students who take the SAT each year receive special accommodations because of documented disabilities. Consider a random sample of 25 students who have recently taken the test. a.) What is the probability...

Hey all i struggling to understand, these concepts. would some explain to me the relationship and differences the distribution of a random variable and a probabiltiy distribution. wikipedia says this about probability distribution "The probability distribution describes the range of possible...

Homework Statement The rejection rate of a certain journal is 45%. If the journal accepts articles at random, what is the minimum number of articles someone has to submit to have a probability of more than 0.75 of getting at least one article accepted? Homework Equations I'm almost sure...

Homework Statement I am trying to find the limits of integration (upper and lower) of a known value of the binomial probability distribution. In other words, I know what the integral (area under the prob. dist.) needs to be (0.84 and 0.16), but how can I code a function (say into MATLAB) that...

Homework Statement Supose that a traffic study measures the speed at which people drive on the highway, and determines that the situation is well modeled by the probability distribution P(v)=Cv4e-v/vo. (a) If we are to measure speeds in mph, give the appropriate units for C and vo. (b) In...

Homework Statement Peter and Paul bet one dollar each on each game. Each is willing to allow the other unlimited credit. Use a calculator to make a table showing, to four decimal places, for each of p = 1/10, 1/3, .49, .499, .501, .51, 2/3, 9/10 the probabilities that Peter is...

i took an exam today and was sort of stumped by this question. pls take a look, thx! how do i interpret this probability distribution: \sum_{k=r}^\infty \binom{k}{r}p^k(1-p)^{k-r} where r is the number of successes, p is the probability, k trials. by looking at it, it seems like...

Homework Statement i have given following problem.I want to know how find an expression for given graph (that is 1st part).rest of parts i will try my self.but with first part i have no idea how to do it. i have attache the word file Homework Equations The Attempt at a Solution...

Homework Statement Assuming 'm' is deterministic the probability distribution of a Random Variable(R.V) r is f(r)=m exp(-rm) Now m itself is a another R.V with a probability distribution g(m). Is it correct to say that now the probability distribution of 'r' is f(r)=E_m [m exp(-rm)] where...

Homework Statement The stationary schrodinger equation for a particle moving in a potential well has 2 solutions psi_1 (x) = e^(-ax^2), with Energy, E_1, and psi_2 (x) = xe^(-ax^2) with Energy, E_2. At t = 0 the particle is in the state psi(x) = psi_1(x) + psi_2(x) a)Calculate the...

If you make an opinion poll over which party people will vote on in a country with seven partys, you get different percentages for the different partys, based on a sample. Say one party has, according to the poll, increased its voters from 5 to 10 percentage points. You want to test if this is...

Homework Statement (Answers: (a) 0.3233 (b) 2 (c)(i) 0.6489 (c)(ii) 0.1669 (c)(iii) 0.2369) Homework Equations Formulae for Discrete Probability Distributions The Attempt at a Solution I don't know how to solve part (b) only. For (b), I have no idea. Is it using...

I have the following equation: \frac{1}{2N^{2}}\int_{s} \int_{p} \left\langle (\textbf{R}_{s} - \textbf{R}_{p} )^{2} \right\rangle which describes the radius of gyration of a polymer. (the term being integrated is the average position between beads p and s) This is shown to be...

Say we have an electron in a position eigenstate \delta(P-x) at point P at time t_0 . We also have a detector at another point Q. At t_0 , the probability of the detector registering the electron is zero. After a certain time T , the time evolution of the wave function generates a...

Hi I have a function \phi =arctan(Y/X) where, X\sim \mathcal{N}(A\cos \theta, v) and Y\sim \mathcal{N}(A\sin \theta,v). I want to find pdf (probability distribution) of \phi . Any suggestions ? I think change of variables in integral might work??

Do linear probability distributions in pure mathematics ever evolve chaotically? In other words, can random statistics tend to reinforce certain singular values nonrandomly? I am reminded of quantum models that favor definite, discrete outcomes.

Find the mean and variance of the uniform probability distribution: f(x) = 1/x for x = 1,2,3,...,n Hint: The sum of the first positive n integers is n(n + 1)/2, and the sum of their squares is n(n + 1)(2n + 1)/6 I know mu/mean will be the sum of products of x and its probability of...

Binomial, Poisson and Normal Probability distribution help! Hey everyone, I've just started a new section on probability (argh) in my math course, and unlike most other maths, I cannot cope! Anyway, I was wondering if anyone could tell me if I did the following question correctly! Any helps...

Homework Statement A box of 10 flashbublbs contains 3 defective bublbs. A random sample of 2 is selcted and tested. Let X be the radom variable associated with the number of defective bulbs in the sample. A) Find the probability distribution of X. B) Find the expected number of...

Homework Statement Stationary Schrodinger equation for a particle moving in a potential well has two solutions psi1(x)=e^-ax^2 with energy E1 and psi2(x)xe^-ax^2 with energy E2 At t=o, the particle is in the state psi(x)=psi1(x)+psi2(x) Calculate the probability distribution as a...

Homework Statement The problem is as shown in the attatchment. Homework Equations The relevant equations are also given in the attatchment. The Attempt at a Solution My problem is how to adapt the given formula in order to find the sum of the function k(40-r) Do i use the...

Homework Statement 2 independent r.v. X and Y, both of them are uniformly distributed on the interval [-1, 1]. a random variable Z is constructed by drawing samples from X and Y and forming X^2 + Y^2, however disregarding any draws that give Z > 1. Show that Z is uniformly distributed on...

[SOLVED]Mean of a probability distribution Homework Statement Homework Equations \int^{b}_{a}p(x)dx=1 V=M_2-\bar{x}^2 \bar{x}^2=\int^{b}_{a}xp(x)dx M_2=\int^{b}_{a} x^2p(x)dx The Attempt at a Solution I found that c=\frac{1}{b} which is a right answer. What I did next...

[SOLVED] Probability distribution function proof Homework Statement Prove the function p(x) = \frac{3}{4b^{3}}(b^{2}-x^{2}) for -b \leq x \leq +b is a valid probability distribution function. Homework Equations I'm not sure if it's as simple as this, but I've been using \int p(x) dx...

Homework Statement 10% of the keyboards a computer company manufactures are defective. 3 keyboards come off the assembly line. Determine the probability distribution, where x=the number of defective keyboards. What would the expected number of defected keyboards be? Homework Equations...

Homework Statement Let's say there are two machines, X and Y. X is connected to Y. * If X is turned on, Y turns on 50% of the time. * If Y turns on (through X being turned on) then it breaks 25% of the time. * Y won't break spontaneously and it can only be turned on through X. What...

Hi, Given the function: P_{k} = \frac{20}{5^{k}} for k \geq 2 How would you prove that P is a probability distribution? I would think that you prove that P is bounded by 0 and 1 (i.e., 0 \leq \Sigma P_{k} \geq 1) And I guess the leading question is how you would prove that a function...

Homework Statement 1. If X, Y, and Z have uniforj density of 1 on unit cube, then find P(X+Y+Z<1) 2. X1, X2, and X3 are independent and normal. Find distribution of Y=(X1^2+X2^2+X3^2)^(1/2) The Attempt at a Solution 1. I set up a triple integral, but I'm not sure if I got the limits...

I have the data set # of freights - probability 1 - .075 1.5 - .025 2 - .425 2.5 - .150 3 - .125 3.5 - .100 4 - .050 5 - .025 6 - .025 The question is, what is the probability that at least 5 of 6 families purchased more than four freights. I started with making a graph of the...

I don't see how this is possible? how can you have a distrubution with no mean? My professor says there is, but i don't get it...

Here is a question that was in on of my exams a few months ago. It asks what is the value of k so that the function f(x;k) is a probability density. I didn't really answer it, but put an answer as k= \frac{1}{2\sqrt{\pi}} because that somewhat resembled the Normal distribution. Does anyone...

I'm reading Basdevant/Dalibard on 'Stationary States of the Hydrogen Atom' in preparation for a final this week, and the "Probability distribution function" for finding an electron in a spherical shell of thickness dr in the ground state is given. It's not derived, so I was wondering if anyone...

I have some homework that I must do, and I have figured out about half of it, but the other half is a complete mystery. I understand the theorems tied to these problems, but cannot do them for some reason or another. Probability distribution for RV X is given by f(x) = { 1/5 for 2 < x < 7...

Hello, What is the dirac delta function and how is it different from a probability distribution?

an urn contains 4 red balls and 4 white balls an experiment consists of selecting at random a sample of 4 balls and recording the number of red balls in the sample setup the probability distribution and compute its mean and variance i know what a probablity distribution is. can someone please...

Is there a way to derive P (X=r) =^nC_r p^r q^{n-r} , r= 0, 1, 2,..., n where X: B(n,p) where n is the total number of bernoulli experiments, p the probability of success q, the probability of failure.

A drawer contains four red socks and two blue socks. Three socks are drawn from the drawer without replacement. a)Create a probability distribution in which the random variable represents the number of red socks. b)Determine the expected number of red socks if three are drawn from the drawer...

gosh this work is causing me some grief, if some one can highlight a few tips i would be greatfull q) determine the probability distribution of the momentum value p in the ground state of the hydrogen atom? i know what the groundstate of the of the hydrogen atom is but i don't know how...

Hi, Sorry about the text, but Latex doesn't work. Can anyone please give me an outline for the derivation of the probability function by inverting its Fourier transform, i.e. P(X>x) = \frac{1}{2} + \frac{1}{\pi} \int_{0}^{\infty} Re \bigg[\frac{e^{-i \theta x}f(\theta)}{i \theta} \bigg]...

Could someone help me to find the probability distribution de XY below ? Take \Omega to be a set of 5 real numbers. Define a probability measure and a random variable X on it which takes the values 1, 2, 3, 4, 5 with probability \frac{1}{10}, \frac{1}{10}, \frac{1}{5}, \frac{1}{5}...

I am trying to compare two probability distributions. I tried the chi-square test, but that requires binned data, and all I have is probability. It seems to work if I ignore the rules about degrees of freedom and just use df=1, but I doubt this is statistically valid. I tried to 'unnormalize' my...

A horse race is going to take place with six runners. The race is over 5 furlongs (1000 meters) and for each of the six contestants it is known that their probable times at this distance are: horse 1: 57.00 sec horse 2: 57.20 sec horse 3: 57.35 sec horse 4: 57.80 sec horse 5: 58.10 sec...

To get at a particle's postion probability distribution we take the modulus of the wave function and square it etc. , but my lecturer said next year we will learn how to get at the particle's momentum probability distribution from the wavefunction, and mentioned something about taking the...

I have the normalized wavefunction u(x)=1/sqrt(L) when -L/2 < x < L/2 and zero everywhere else. I want the value of p when the probability of getting a measurement result close to p i maximal/minimal. I seek for maximum/minimum probability density! I was thinking of Fouriertransform u(x)...

when you calculate the Moment of the following equation p(x)=\left\{\begin{array}{cc}2Axe^{-Ax^2},&\mbox{ if } x\geq 0\\0, & \mbox{ if } x<0\end{array}\right. We get Mn =2A \int_0^\infty x^{n+1}e^{-Ax^2} solving it by parts I am getting...

I hope someone can help me understand functions of random variables: If X~Uniform(A,B), A < X < B Y~Normal(0,1), -inf < Y < inf and Z = X + Y - what is the pdf of Z? - how can I calculate a probability like P(Z < 3)? - what is the conditional probability P(Z<z | X = x)? - what is the...

Given the probability distribution function f(x) = \frac{2}{9}(x-1), -1<x<2 find the pdf of Y = X^2 My Solution: When x = -1, y = 1 and when x = 2, y = 4, so the range of y is 1 \leq y \leq 4 So to find the pdf of Y = X^2, we need to find the cdf of Y. Since...

Hi, I just started a physical chemistry class and we are working on probability theory. The questions I am having a hard time with are as follow: we are given that E is proportional to exp[-E/RT]. It is stated that this is a simple system having only four energy states numbered 1 through 4...