Statistics Definition and 998 Threads

Homework Statement The problem I have been set is to rework the Drude model using clearly defined scattering statistics. Homework Equations The Drude model as we have been given it is in terms of momentum \vec{p}(t+dt)=(1-\frac{dt}{\tau})(\vec{p}(t)-q\vec{E}(t)dt)+(\frac{dt}{\tau})(0) Where...

Homework Statement An engineer is measuring a quantity q. It is assumed that there is a random error in each measurement, so the engineer will take n measurements and reports the average of the measurements as the estimated value of q. Specifically, if Yi is the value that is obtained in the...

Homework Statement The number of customers visiting a store during a day is a random variable with mean EX=100and variance Var(X)=225. Using Chebyshev's inequality, find an upper bound for having more than 120 or less than 80customers in a day. That is, find an upper bound on P(X≤80 or X≥120)...

Homework Statement Let X∼Geometric(p). Using Markov's inequality find an upper bound for P(X≥a), for a positive integer a. Compare the upper bound with the real value of P(X≥a). Then, using Chebyshev's inequality, find an upper bound for P(|X - EX| ≥ b). Homework Equations P(X≥a) ≤ Ex / a...

Homework Statement Let X1 and X2 be independent normal random variables, distributed as N(μ1,σ^2) and N(μ2,σ^2), respectively. Consider a random variable U = 2X1 − X2. (a) Find the mean of U. (b) Find the variance of U. (c) Find the distribution of U. The Attempt at a Solution a) E(U) =...

Homework Statement If M[X(t)] = k (2 + 3e^t)^4 , what is the value of k Homework Equations M[X(t)] = integral ( e^tx * f(x) )dx if X is continuous The Attempt at a Solution I tried differentiating both sides to find f(x), but since it is a definite integral from negative infinity to infinity...

One hundred pennies are being distributed independently and at random into 30 boxes, labeled 1, 2, ..., 30. What is the probability that there are exactly 3 pennies in box number 1? I tried using a Poisson distribution f(x) = (e^-λ)*(λ^x)/x! , with λ = 100/30 = 10/3 and x = 3. I got 0.22021 (5...

Homework Statement Given X,Y,Z are 3 N(1,1) random variables, (1) Find E[ XY | Y + Z = 1] Homework EquationsThe Attempt at a Solution I'm honestly completely lost in statistics... I didn't quite grasp the intuitive aspect of expectation because my professor lives in the numbers side and...

If the moment generating function for the random variable X is M[X(t)] = 1/(1+t), what is the third moment of X about the point x = 2? The general formula only states how to find moments about x = 0. Thanks!

hi. please help. `im searching for an android app for bingo statistics. there is a tv game for bingo. each week there is a game you choose 20 numbers (4 numbers in each row) from 75. if someone using one, would be thankfull to hear from you. thanks in advance

Homework Statement Find the formula for the standard deviation (s_h) of heading angle, given the north and east standard deviation of position of two points (s_n1, s_e2, s_n2, s_e2), each point's north-east covariance (s_cov_ne_1, s_cov_ne_2) and the north and east distance between them (d_n...

Homework Statement Given a Uniform Distribution (0,1) and Z = X/Y Find F(z) and f(z) Homework EquationsThe Attempt at a Solution So I'm just trying to make sure i have the range correct on this one... I'm honestly lost from beginning to end with it. R(z) = {0,∞} because as y is very small, Z...

There are two series on a graph, series A is the prediction of a value over time, series B is a curve of observed values over time. How can one quantify how much series A resemble series B?

Homework Statement E = { (x,y) | |x| + |y| ≤ 1} fx,y (x,y) = { c (x,y) ∈ E 0 otherwise } Find C. Find the Marginal PDFs Find the conditional X given Y=y, where -1 ≤ y ≤ 1. Are X and Y independent. Homework Equations I'm taking a guess here in the solution... but F(x,y) = F(x)F(y) and...

Homework Statement given set C = {(x,y)|x,y are integers, x^2 + |y| <= 2} Suppose they are uniformly distributed and we pick a point completely at random, thus p(x,y)= 1/11 Homework Equations Listing it all out, R(X) = {-1,-2,0,1,2} = R(y) The Attempt at a Solution My problem is that when I...

Homework Statement Suppose that object 1 weighs \theta_1 and object two weights \theta_2. Then each object is weighed once and then together getting three observations y_1,y_2,y_3. The scale gives unbiased weights with normally distributed error (constant variance) Find the least square...

Does anyone have an intuitive idea for the statistics of chaotic light? I can understand that the power fluctuations in this kind of light can give rise to a second order autocorrelation parameter g(2) higher than 1. However I can not see why the value for this parameter should be g(2)=2. Does...

Homework Statement Consider two random variables X and Y with joint PMF given by: PXY(k,L) = 1/(2k+l), for k,l = 1,2,3,... A) Show that X and Y are independent and find the marginal PMFs of X and Y B) Find P(X2 + Y2 ≤ 10) Homework Equations P(A)∩P(B)/P(B) = P(A|B) P(A|B) = P(A) if independent...

Please can anyone tell me what is optimistic cost and what is pessimistic cost. You may suggest a book or a link where I can find explanation. I have tried to search for it but could not find anything useful. I want to solve the questions shown below. I will be grateful to you for your help. Thanks

The assignment was already turned in a while ago, but I am currently reviewing all the past homework and trying to resolve the problems I couldn't understand. The website software gives the correct multiple choice or numerical answer, but not the steps. They gave me a weird answer and I didn't...

A manufacturer has designed a process to produce pipes that are 10 feet long. The distribution of the pipe length, however, is actually Uniform on the interval 10 feet to 10.57 feet. Assume that the lengths of individual pipes produced by the process are independent. Let X and Y represent the...

Hi All, I know that to prove oneself to employers in programming, one can try to contribute to open source projects or just make e.g. your own game. Is there something analogous for statistics? I am studying a mathematics and statistics honours degree part-time (I work) and by distance...

Homework Statement An article suggests that a Poisson process can be used to represent the occurrence of structural loads over time. Suppose the mean time between occurrences of loads is 0.4 year. a). How many loads can be expected to occur during a 4-year period? b). What is the probability...

could we say like the title that if we throw coins n times the result were s=nhead/n this were statistics and we could find a prediction for the next toss p(s)=? I thought we could reason like : the next tosses shall equilibrate towards 1/2 so for example p(s)=1-s ?

I run a photo contest that uses a 5-star rating system which ranks the images according to their average rating. However, I would like to factor in the total number of votes a photo receives to get a more accurate ranking. For example, I do not want an image with one 5-star vote (Avg rating: 5)...

I hope this is the right place to post this, please move if you think it's needed. I want to ask how do I extrapolate a correlation from a bunch of numbers. I did and experiment on gyroscopes, and have three kinds of data, w1, w3 and F_t, the later two can be used to calculate L3 and T_g. My...

Homework Statement X ~ Uniform (0,1) Y = e-X Find FY (y) - or the CDF Find fY(y) - or the PDF Find E[Y] 2. Homework Equations E[Y] = E[e-X] = ∫0 , 1 e-xfx(x)dx FY(y) = P(Y < y) fY(y) = F'Y(y) The Attempt at a Solution FX(x) = { 0 for x<0 x for 0<x<1 1 for 1<x } fX(x) = { 1 for...

Hi all, I've been thinking about bioinformatic and biophysical problems, and have noticed that notions of symmetry keep cropping up. An obvious example would be protein conformational change, since the correlations between atoms induce reductions in the entropy of the system via degeneracy...

Homework Statement Suppose you take a pass-fail test repeatedly. Let Sk be the event that you are successful in your kth try, and Fk be the event that you fail the test in your kth try. On your first try, you have a 50% chance of passing the test. P(S1)=1−P(F1)=1/2. Assume that as you take the...

Homework Statement 50 students live in a dormitory. The parking lot has the capacity for 30 cars. If each student has a car with probability 12 (independently from other students), what is the probability that there won't be enough parking spaces for all the cars? Homework Equations P(A) =...

Which B.S degree is more employable : finance or statistics (Business emphasis)?

Homework Statement For reference, this is the image setting up the problem. "A wireless sensor grid consists of 21×11=231 sensor nodes that are located at points (i,j) in the plane such that i∈{0,1,⋯,20} and j∈{0,1,2,⋯,10} as shown in Figure 2.1. The sensor node located at point (0,0) needs...

I'm a statistics major, due to engineering not being feasible (units) at this point, and that I'm not really interested in anything in particular that much.. Statistics seems like a degree that is neither too shabby or too good in terms of employ-ability, so it seems reasonable. my goal after...

Homework Statement http://prntscr.com/8ea2rk Homework Equations In statistics, when testing hypothesis for both sides (left and right), is it possible that Xaverage - MUo = 0 (upper part of the equation I provided)? If so how to solve this kind of task? The Attempt at a Solution If I get...

Homework Statement If you have a 52card deck and split it evenly to 4 people (a,b,c,d) then what is the probability that persons a and b have 7 spades and person c has 3 spades. Homework Equations P(A) = |A|/|S| The Attempt at a Solution I divided up the decks 4 ways. So Persons a and b...

Homework Statement In a 52 card deck, if you draw 5 cards find the probability of drawing exactly one ace. Homework Equations (n k) = n!/k!(n-k)! P(A) = |A|/|S| The Attempt at a Solution So I took the logic of a different example we had that stated it like this - If we have 5 options but...

With just a BS, what kind of jobs could I get with a BS in Statistics (with business emphasis)? With a BS in statistics (with business emphasis) or a BS in Business Administration (with concentration in decision science/operations research) be more employable?

Homework Statement Let X be a continuous random variable with cumulative distribution function given by F(x) = P(X<x). Define a new random variable U=F(X). Homework EquationsThe Attempt at a Solution OK so to solve this problem I first say U=F(X). F(u)=P(F(X)<u) which means F(u)=P(U<u) is...

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...

Homework Statement Problem Consider a random experiment with a sample space S={1,2,3,⋯}. Suppose that we know: P(k) = P({k}) = c/(3^k) , for k=1,2,⋯, where c is a constant number. Find c. Find P({2,4,6}). Find P({3,4,5,⋯}) I am primarily interested in part 1, finding C. The rest...

Homework Statement Let A and B be two events such that P(A) = 0.4, P(B) = 0.7, P(A∪B) = 0.9 Find P((A^c) - B) 2. Homework Equations I can't think of any relevant equations except maybe the Inclusion Exclusion property. P(A∪B) = P(A) + P(B) - P(A∩B) This leads us to another thing P(A∩B^c)...

Homework Statement In my statistics notes/lectures my professor will oftentimes use an identity that looks like the following: x_i is a non random variable, the summand is from i=1 to n; This segment comes from notes on linear regression (y_0 = b_0 + b_1*x_i) I actually forgot to mention that...

Could you please list and elaborate as much as you can on schools that are heavy on the theoretical side of statistics? Thank you as I have to have my applications in by December-January for grad school (I plan to enter a PhD program and would like guaranteed funding).

What is a fantastic book on probability&statistics that covers all the probability&statistics a student in high school ever need? It should cover the basics, and also the intermediate topics. Specifically, it must cover frequency distributions and whatnot. Please lend me your suggestions.

Homework Statement that it is exact... [/B] X and Y are discrete random variables with joint pmf Chart attached (a) Find V ar(X) and Var(Y). (b) Find Cov(X; Y). (c) Find the correlation of X and Y. (d) Find the conditional distribution of X given that Y= 3 Homework Equations...

I am having trouble proving that two multivariate formulas are equivalent. I implemented them in MATLAB and numerically they appear to be equivalent. I would appreciate any help on this. Prove A = B A = (Σπ^-1 + Σy^-1)^-1 * (Σπ^-1*π + Σy^-1*y) y = π+ X*β Σπ =τ*Σ Σy = X' * Σβ * X + ΣεB =...

HI everyone. I was just wondering about a career in the IT (I study communication systems engineering, but I'm rather interested in coding, rather than Internet and communcation systems- related stuff). I wanted to ask you, given the advances that technology is making, which skills would be...

Sorry if this is in the wrong section. I didn't know which homework section I should use. 1. Homework Statement Human subjects are involved in a medical study to represent certain segments of the population in terms of blood lead concentration, PbB. First, assume the normal distribution...

Do we have Bose like and Fermi like particles (fields) in 1+1 dimensional spacetime, Fermi like particles (fields) that obey the Pauli Exclusion Principle? For what space dimensions does the Pauli Exclusion Principle operate? Thanks for any help!

It's hard to type this out as there is a diagram and notation I can't find on the key board so I've attached an image of the question and answer. I've explained my solution below however I've also attached an image if it's too confusing with the lack of symbols! Problem involves uniform...