Mathematics Stack Exchange
Mathematics Stack Exchange

Questions tagged [statistics]

Mathematical statistics is the study of statistics from a mathematical standpoint, using probability theory and other branches of mathematics such as linear algebra and analysis.

Statistics is the science of the collection, organization, and interpretation of data. It deals with many aspects of data, which includes the planning of data collection in terms of the design of surveys and experiments. (From Wikipedia)

More specifically, mathematical statistics is the study of statistics from a mathematical standpoint, using probability theory as well as other branches of mathematics such as linear algebra and mathematical analysis. (From Wikipedia)

For questions which are more generally about collecting and treating data, it is advised that you post your question on Cross Validated and DSSE.

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How to calculate R-square from adjusted r-square, n, and p?

Let $\bar{R}^2$ denote the adjusted coefficient of determination. I have $\bar{R}^2 = 0.9199$ with 15 cases. Now I am trying to find $R^2$ given the results below. I found the formula for $R^2$ but did not understand it. How do you calculate $R^2$…
hhh
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This is regarding Chi square test

A chi square test is conducted to check whether a person's ability in Mathematics has an impact on his/her interest in Statistic. The test statistic is 13.277 under the tested null hypothesis. write a recommended null hypothesis and an alternative…
ChampR
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Continuous random variable question

$ X $ is a non-negative continuous random variable with density function $f$ and distribution function $F$. Use integration by parts to show that $ \int_0^{\infty} ( 1- F(x)) dx = \int_0^{\infty}xf(x)dx $ I'm quite puzzled on how to even…
neverloggedin
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How do I prove that a statistic is a pivot?

In this example I have a sample out of a distribution with density $P_{\theta}(x) = 2x^{\theta} e^{−\theta x^2} I_{x \ge 0}$. I know that for all $i \ge 1$ we have $X_i^2 \sim Exp(\theta)$. If $\theta = 1$, then $T_1 = 2\sum_{1 \le i \le n}X_i^2…
Laura van Leuven
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Is there a Central limit theorem for max

I have multiple IID (bigger then 0) of unknown distribution and I get the max of them as a result of my calculation. Can I say that the max also have certain gaussian shape distribution? If not what is the distribution of the result? I saw this…
user158881
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how to tell whether x and y are independent or not

Suppose that $f_{x,y}(x,y) = \lambda^2 e^{\displaystyle-\lambda(x+y)}, 0\leq x , 0\leq y.$ Find $\operatorname{Var(X+Y)}$. I'm having trouble with this problem the way to find $\operatorname{Var(X+Y)} =…
notamathwiz
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Combination calculation with reducing set size

My statistics aren't too great, so I'm struggle to work out the result of the following situation. Say you have 5 sets of 5 possible options (25 options total); and you select 1 option from each set. Each time you select 1 option from a set, that…
Ben Lessani
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Finding the mle of a log normal distribution

So let $X1,X2,..,XN$ be an independent sample from log normal distribution with the pdf $f(x,\theta)=(x^2 \sigma^2*2\pi)^{(-1/2)}e^{-(log(x)-\theta)^2/{2\sigma^2}}$ and we have $\sigma^2=1$ and $\theta$ uknown So I did the following we have…
Fernando Martinez
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Averages clarifications!

If i know an average such as ( catch an average of one rat every 39 minutes ) what is the average number of rats caught in 10 hours ? is it as simple as dividing 600/39 (600 = 10 hours in minutes) and multiplying this value by number of rats caught…
Dark 21
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First order Autoregressive model

How do I solve this? How can I obtain the lag-one autocorrelation coefficients just from the data?? Following are $10$ years of observation of annual streamflows in millions of cubic…
Fung Chun Chun
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consistency of MLE estimator example

Given the density function $f(x;\theta)=\theta x^{\theta -1}$ with $\theta \gt 0$ and $x \in (0,1)$, once found the MLE estimator $\hat{\theta}=\frac{-n}{\sum{\log{X_i}}}$ i want to show the consistency of such an estimator. I was suggested to apply…
Mattiatore
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How to calculate the variance of this maximum likelihood estimator

Suppose my likelihood function is (multiplication of $n$ Poisson function with $\lambda=\mu x$): $$L(\mu;x)=(e^{-\mu x})^a(1-e^{-\mu a})^{n-a}$$ I have calculated $$\log L=-a\mu x+(n-a)\log (1-e^{-\mu…
JFK
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If you choose two different sets of results to match inside a coin flipping record, does the odds of finding a match depend on what you pick on each?

Example, if you flip a coin 10 times and record the results, and you pick 2 different sets of 5 length (e.g HHTHT and TTHTT where H=heads and T=tails) and the goal is to match any of your two sets anywhere inside the coin results (e.g TTTTHHTHTH…
ajax333221
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How many games will you play and how many of those games will you lose?

Each time you play a game, you win with probability p. (The games are independent.) You plan to play 5 games, but if you win the fifth game, then you will keep on playing until you lose. (a) Find the expected number of games that you play. (b) Find…
David Nam
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Determining a proper sample size in binomial distribution

An agency is holding a poll, where each participant can either support or not support some upcoming motion. We model the answers with i.i.d. Bernoulli variables for which $X = 1$ means to support the motion with probability $P(X = 1) = p$. We'd like…
Epsilon Away
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