What is Mathematical statistics: Definition and 16 Discussions

Mathematical statistics is the application of probability theory, a branch of mathematics, to statistics, as opposed to techniques for collecting statistical data. Specific mathematical techniques which are used for this include mathematical analysis, linear algebra, stochastic analysis, differential equations, and measure theory.

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1. What is the correct formula for the reduced Chi square?

Hi all I want to calculate the reduced Chi square and root mean square deviation RMSD of some data points that i have, but I am confused about the correct formula for each of them, which one is the correct one. I found this formula in a paper where they referred to it as the RMSD : ...
2. A Recalculate a range by variable 'Median'?

Hello everyone :) I'm struggling to wrap my head around recalculating a data set based upon median. The data set represents a fixed distribution pattern of population to income group. There is no data available for 'population to income group' at differing medians, hence we accept the...
3. Simple ##\chi^2## Tests for Weighted Averages and Linear Regression

1. Suppose one has the measurements [1.20, 1.15 ,2.0 ,1.17] with uncertainties [0.2,0.1,0.8,0.07]. Then, if ##E## is the weighted average, is it correct that ##\chi^2## is simply given by ##\sum \frac{(O-E)^2}{E} \ ?## 2. If one has | x | y | | -- | -- | | 0 | 0 ##\pm## 1 | | 1 | 1 ##\pm##...
4. (2/3) as constant factor In Kinetic theory of gases

Hi I'm in high school but what I'm going to ask you is probably being teached in college. General formula: p=(2/3)*(N/V)*Ek p- pressure N- amount of molecules V- volume of the container Ek - AVERAGE kinetic energy I've been told by my physics teacher, that 2/3 constant factor in kinetic theory...
5. Probability or Mathematical Statistics?

I am a Mathematics and Chemistry major with a Physics minor. I need to take one more mathematics elective course next semester. I had two picked out but both unfortunately overlap with other classes I am taking, so I am now trying to choose between Probability or Mathematical Statistics (course...
6. Prove Chi Square is Stochastically Increasing

Homework Statement Prove that the X^2 distribution is stochastically increasing in its degrees of freedom; that is if p>q, then for any a, P(X^2_{p} > a) \geq P(X^2_{q} > a), with strict inequality for some a. Homework Equations 1.(n-1)S^2/\sigma^2 \sim X^2_{n-1} 2.The Chi squared(p) pdf is...
7. Best book on mathematical statistics

Hi Please advice me a good book on mathematical statistics.I want it to be oriented in math students or engineering level. Best Regards
8. Mathematical Statistics Xi~N(6,25) P[1.860 < 3(Xbar - 6]/S

Homework Statement Let X1, X2, ..., X9 be a random sample from a normal distribution, Xi~N(6,25), and denote by Xbar and S^2 the sample mean and sample variance. Use the standard statistical table for normal distribution. Homework Equations E[S^2] = δ^2 = 25 S^2 = (ƩXi^2 -...
9. Mathematical Statistics good for Computer Scientists?

I am finished with the first bachelor year at Computer Science and the next courses are: Assembly, Linear Algebra, Statistics, Java. Many people from my class said that they will not take Statistics as it's not that helpful to them and I was thinking of how accurate that is. Is Statistics...
10. Mathematical Statistics question

Homework Statement let X be a random variable with uniform p.d.f over the interval (0, theta) Determine whether 2X-bar (sample mean) is an unbiased and consistent estimator for theta Homework Equations bx(theta)=EX-theta The Attempt at a Solution By using normal...
11. Difference between applied statistics and mathematical statistics.

What is the difference between applied and mathematical statistics ? Does applied statistics skip a great deal of necessary knowledge ? Is applied statistics enough to construct statistical models?
12. Mathematical Statistics- two sample t-test

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...
13. How important is probability and mathematical statistics?

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...
14. MSc in Mathematical Statistics.

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...
15. Mathematical statistics

Homework Statement let f(x) be a density on R+ (so f(x) < 0 if x < 0). Let g(x,y) = f(x+y)/(x+y), x > 0, y> 0 a) show g is a density on R^2 b) assume that the expectation u and variance sigma^2 associated univariate density f exist and that mu^2 does not equal 2sigma^2. Show that X and Y...
16. Any thoughts on Introduction to Mathematical Statistics by Hogg, Craig, and McKean?

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...