Statistics Definition and 998 Threads

Homework Statement At the 5% level, will the two means be equal ? Homework Equations The Attempt at a Solution I tested the variances and found out that it's very likely that the variances are equal, so this is an assumption we make when we do the second test. Now, I'm trying...

Ok so my question is as follows: Can Maxwell Boltzmann statistics be used to describe electrons in a metal at room temperature? I know that the Fermi Temperature in metals is about 10^4 K or something rather high, so does that mean that the metal / electron gas would need to be at a...

Hello everyone, I'm currently deciding where I should study next year, and I would appreciate any advice you could give. I am a Canadian citizen, and I just finished my bachelors with a physics/statistics double major. My long term goal is to research machine learning, either in a faculty...

I'm a senior undergrad student and I am going to give a 50 minute lecture on Degenerate Fermi Gases to the Thermodynamics and Statistical Mechanics class. I was wondering if anybody could help me out with coming up with some interesting stories, factoids, thought experiments, history lessons...

Homework Statement Consider the distributions N(mu1, 400) and N(mu2, 225). Let theta = mu1-mu2 and x and y be the observed means of two independent random samples, each of size n, from these two disbtibutions. We reject H(0) : theta = 0 and accept H(a): theta >0 if and only if x-y >=C. If...

Homework Statement A u-shaped tube open to air at both ends contains some mercury. A quantity of water is carefully poured into the left arm of the tube until the vertical height of water is 15 cm.Homework Equations (a)What is the gauge pressure at the water-mercury interface?[ans 1.47*10^3Pa]...

Right, the question is how much Stats do I need? I am aiming for a double major in Math and Physics I know that at some point I will have to take First-year stats (AP Statistics?), but what is beyond that? How many of those permutations/combinatorial courses will I need? By the way, I am a...

Suppose that the mean score of a class of 30 students was 78. The 19 male students in the class had a mean score of 68. What was the mean score for the 11 female students? advice? thanks.

Hello friends! Given an estimator of the population mean: \bar{Y}=\frac{\sum^{N}_{i=1}Y_{i}}{N} The expected value of \bar{Y} is : E(\bar{Y}) = \frac{1}{N}E(Y_{1})+\frac{1}{N}E(Y_{2})+\cdots+\frac{1}{N}E(Y_{N})=\mu where \mu is the population mean. Therefore: E(\bar{Y}) =...

Homework Statement A plant manufactures 500 components a day with the diameter being random variable: N(8.02, 0.1^2)mm What is the probability of two randomly picked components differing by more than 0.3mm?2. Solution I know that the solution is 0.966The Attempt at a Solution I thought that I...

Hello, a very interesting forum you have here:) So, to business The topic says it all - I'm looking for a good textbook for undergraduate on probabilities and mathematical statistics. Could you recommend something? I thought about: First Course in Probability by Sheldon Ross, but I have read a...

Homework Statement X is a discrete random variable that has a Poisson Distribution with parameter L. Hence, the discrete mass function is f(x) = L^{x} e^{-L} / x!. Where L is a real constant, e is the exponential symbol and x! is x factorial. Without using generating functions, what is...

Today in class, by the existence of an operator that exchanges the states of two indistinguishable particles, we attempted to derive the existence of fermions and bosons & how this relates to the symmetries of multiparticle wave functions. The argument given in my textbook is: define an...

I have a degree in Engineering. Now I am back to school, for a 2 year Master's degree in Statistics. The second semester just started. And there will be a 3rd. Is there a chance that I will need complex numbers? My background in Complex Analysis is very limited. Should I study any Complex...

Homework Statement Suppose that n=5 observations are taken from the uniform pdf, fY=1/\Theta 0<y<\Theta where \Theta is unknown. Two unbiased estimators for \Theta are \Theta1= (6/5)*Ymax \Theta2= (6)*Ymin which estimator would be better to use? hint: What must be true of Var(Ymax) and...

Homework Statement There is some question, I solved it but am not sure I got the right answer. Let Y1, Y2... Yn be a random sample of size n from the pdf fY(y;\Theta= \frac{1}{\Theta}*e-y/\Theta , y>0 Let \Theta_hat=n*Ymin is tex]\Theta[/tex]_hat for \Theta ? Homework Equations...

I'm a sophomore in math.I intend to learn mathematical and physics something like differential geometry,topology and QFT in my next years and do some research in some relative topics.I know I need to learn many courses and I feel I don't have enough time.This semester we open a course called...

Homework Statement A random sample of size 2, Y1 and Y2, is drawn from the pdf fY(y;\vartheta)=2y*\vartheta2, 0<y< 1/ \vartheta What must c equal if the statistic c(Y1+2Y2) is to be an unbiased estimator for 1 / \vartheta Homework Equations The Attempt at a Solution I tried...

Homework Statement Two cards are drawn from a standard deck with replacement. A=first card is an ace. B=second card is an ace. Show that A and B are independent Homework Equations P(A and B)=P(A given B)/P(B) P(A given B)=P(A) The Attempt at a Solution P(A)=4/52 P(B) =4/52 P(A...

URGENT help needed with statistics, probability Homework Statement 1) A plane functions iff at least 2 of its 3 engines function. P(each engine functions)=p, the engines operate independently of each other. Find the probability that the plane functions. The Attempt at a Solution...

1) Distribution is a uniform distribution on the interval (Ө, Ө+1) Show that Ө1 is a consistent estimator of Ө. Ө1=Ῡ -.5 Show that Ө2 is a consistent estimator of Ө. Ө2=Yn – (n/(n+1)). 2) I think the distribution for this one is a uniform distribution on the interval (0, Ө) but...

Well the questions and solutions are in one for some and I will type out the rest. Q6 http://img249.imageshack.us/img249/2757/47026197.jpg Q4 http://img237.imageshack.us/img237/1802/93774799.jpg Q3 http://img3.imageshack.us/img3/5919/34981698.jpg Q1...

Homework Statement The electricity usage (KWh) in homes was studied over a period of time. For Year 1: Mean = 1130 Std dev. = 196 n = 16 For Year 2: Mean = 1350 Std dev. = 302 n = 21 a) Test the hypothesis that the std dev. in year 2 has increased compared to year 1...

Hi there, I have a question regarding infinity and statistics. (I hope there aren't too many questions with infinity on these forums) I was wondering if you had some simple procedure, like say rolling a six sided die, and said you did this an infinite amount of times, would it be valid to...

Homework Statement In the Drude model the probability of an electron having a collision in an infinitesimal time interval dt is given by dt/\tau. (a) Show that an electron picked at random at a given moment will have no collisions during the next t seconds with probability e-t/\tau. (b) Show...

Hey everyone! Spring semester recently started for me and I am really getting stressed out as I am trying to lay a solid plan for my future. First, a bit of information about myself: Sophomore honors student at a pretty decent state school. B.S. in Mathematics and Economics (4.0 GPA in...

***SOLVED*** Homework Statement A system of particles is at equilibrium. What is the proportion of particles in the ground state? The Attempt at a Solution P(\epsilon_{s})=\frac{exp(-0/\tau)}{1+exp(\frac{-\epsilon_{s}}{\tau})+exp(\frac{-2\epsilon_{s}}{\tau})} Is that right? This is a...

Greetings I became interested in technical sciences only last year (I'm a historian) and started studying on my own. Just finished Multivariable Calculus and Linear algebra with Paul's online math notes. (for those who may know about this page yet: http://tutorial.math.lamar.edu/) Now I'm...

Homework Statement It's problem 1. (b) in the attachment. I need help finding the average number of records. Note: Obviously, I'm not actually in the class. I just got bored and started going through the course assignments Homework Equations From the first part of the question, I...

Hey all, I will soon be graduating with a MSc in Transportation Engineering. I'm currently writing my thesis, and probably by May 2010 will be done. However, I am unsure I am willing to go for a PhD, at least not in this field. During my time in my Master, I found out I can only do...

Not sure if this is much of guidance, but seemed to be the best category? Is there a place where I can check nationwide statistics for Undergraduate Physics enrollment? I know that Physics I and II always have a good enrollment of 15-25 students, but as soon as it crosses that upper level...

Can a photon gas undergo a Bose Einstein condensation ?

I want to study it myself recently ~but I don't know where to start ? Can anyone help me ? XD

"the probability to buy a suite is 0.22 the probability to buy a shirt is 0.3 the probability to buy a tie is 0.28 the probability to buy a suite and shirt is 0.11 the probability to buy a suite and tie is 0.14 the probability to buy a tie and shirt is 0.28 what is the probability that...

Homework Statement Consider an atom with a magnetic moment \mu and a total spin of ½. The atom is placed in a uniform magnetic field B at temperature T. (a) Assuming Maxwell-Boltzmann statistics are valid at this temperature, find the ratio of atoms with spins aligned with the field to those...

For the following tests of significance 1 tests of mean difference for paired data - differences a calulated - forms a new random variable test its mean 2 two sample normal tests - looks at the differences in averages i have trouble picking which one to use for problems, i mean...

Im currently doing an introductory stats course and have learnt: - poisson distribution - binomial distribution - normal distribution - t-student - and chi-square I think I know what most of them look like but am having a bit of a hard time distinguishing what distribution to use when...

Homework Statement Let X1,X2,X3,Y1,Y2,Y3 be random variables. If X1 and Y1 have the same distribution, X2 and Y2 have the same distribution, X3 and Y3 have the same distribution, then is it true that X1+X2+X3 and Y1+Y2+Y3 will have the same distribution? Why or why not? 2. Homework...

Theorem: Let {N(t): t≥0} be a Poisson process of rate λ. Suppose we are given that for a fixed t, N(t)=n. Let Ti be the time of the ith event, i=1,2,...n. Then the (conditional) density function of Tn given that N(t)=n is the exactly the same as the density function of X(1)=min{X1,X2,...,Xn}...

The question reads exactly as follows, Find the appropriate values for #'s. a) P(Z<#)=.9 b) P(|Z|<#)=.9 We are currently going over distributions, poissons, density functions and binomial stuff, someone referenced to Z-values from a ztable but i don't know if this is what the topic...

Hello, Suppose that we have the following set of independent and identically distributed RVs: \gamma_1,\,\gamma_2,\,\ldots,\,\gamma_M. Arranging them in descending order as: \gamma_{1:M}\ge\gamma_{2:M}\ge\cdots\ge\gamma_{M:M}. Now suppose we select the largest m\leq M order statistics. What...

1) My wife and I are very athletic. Between us, we jog an average of 5 miles a day. My wife jogs 10. 2) In freeway driving, my car averages 32 miles per gallon. 3) Last year my car repairs averages $48 per month. 4) The average statistician has 3.46 children. 5) The average fuse time...

I am having trouble with what seems to be a simple combinations or permutations problem as follows: Melodies for more than 14,000 songs are listed according to the following scheme" The first note of every song is represented by anasterisk * and successive notes are represented by R (for repeat...

Biting an unpopped kernel of popcorn hurts! As an experiment, a self-confessed connoisseur of cheap popcorn carefully counted 773 kernels and put them in a popper. After popping, the unpopped kernels were counted. There were 86. How do I do this? (a) Construct a 90 percent confidence...

Would you agree that statistics can be mathematically misrepresented to prove most related arguments both true and false?

Really stuck on this question. Stock A has an expected return mean of 0.03 and standard deviation of 0.02 Stock B has an expected return mean of 0.02 and standard deviation of 0.01 Investor invests in 20 lots of stock A and 15 lots of Stock B (as in 4/7 in A and 3/7 in B) What is the...

Hello all, we have the B-E function <n>=1/(exp(x)-1), where x is hv/kT. What is <n> actually? because i ready everywhere that it is average no. of phonons! but it also probability..? Please explain clearly all terms involved in the above relation.. thanks

Homework Statement not exactly sure were this goes ok there was a question that my teacher told me i got wrong the question asked me to compute the mean which I did... then the question went on to tell me compute the mean with another observation equal to zero then the part that...

Hello. Does anyone here have some resources about "probability and statistics for biomedical engineers" or "probability theory","random processes" ? I do need it. Thanks in advance!

Any thoughts on "Introduction to Mathematical Statistics" by Hogg, Craig, and McKean? Dear PF members, I was looking for a textbook for my mathematical statistics course, and it turns out that Introduction to Mathematical Statics by Hogg, Craig, and McKean will be the book for the course...