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.

37109 questions
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can I get the correct average of a set of numbers from the averages of several subsets?

Let's say I have this set of numbers: 565 212 812 895 443 73 468 900 299 993 252 740 291 112 (average 503.9285714286) I'd like to split them apart into 3 sets of unequal size: 565 212 812 (529.6666666667) 443 73 468 900 299 895 (513) 993…
jcollum
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World Cup Group prediction probability

We have an office world cup bet where each person guesses the team that finishes 1st and 2nd from their qualifying group. E.g. A1: Brazil A2: Mexico B1: Netherlands etc... You get a point for every correct guess. The person with the most points…
harryg
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The p.d.f as a derivative of the c.d.f.

The cumulative distribution function is defined as: $$F(x)=P(X\le x)=\int_{-\infty}^x f(t)\,dt,$$ where $f(t)$ is the probability density function. By the fundamental theorem of calculus: $$f(x)=F'(x)$$ I am having some difficulty with this topic.…
David
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How to show that two multivariate normal distributed random variables are independent?

Let $X\sim N(\mu_1,V_1),~~Y\sim N(\mu_2,V_2)$. How can I show that $X$ and $Y$ are independent? I am wondering how I can show this. I only know the following case: $Z=(Z_1,\ldots,Z_n)\sim N(\mu_3,V_3)$: Then $Z_i$ are independent if…
user34632
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How to analyze risk vs. reward for spending on research and development work?

Imagine I have a company that makes widgets, where each widget costs me A dollars to make. Each month I can allocate money toward research and development with the aim of finding a new process that will allow me to build widgets for a cost of A/B…
Scott Mitchell
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Calculating a Fisher expected information

Let $X_1,..., X_n$ be a random sample from a distribution with probability density function $f(x;\theta) = (1/2\theta) exp(-|x|/\theta)$ for $-\infty
Brian
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How do percentiles work?

If I have 5 students (A-E) that score 80%, 70%, 70%, 60% and 50% on a test what percentiles do they fall in? A - 20th percentile (80%) B - 40th percentile (70%) C - 40th percentile (70%) D - 80th percentile (60%) E - 100th percentile (50%) Is this…
Guy
  • 169
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Show that $Var(\theta_1)>Var(\theta_2)$.

I calculated that $$ Var(\theta_1)=\frac{2\sigma^2}{(x_n-x_1)^2},~~~~~Var(\theta_2)=\frac{\sigma^2}{\sum_{i=1}^{n}(x_i-\overline{x})^2}. $$ Now I have to show that for $\sigma^2 >0$ and $\overline{x}\neq\frac{(x_1+x_n)}{2}$ it is …
mathfemi
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Need to check if a t- test should be used instead of a z -test here!

For this question shouldn't they be using a t test and the test statistic should be t and not z as the sample is small? Is this a mistake in the mark scheme?
user134785
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Degrees of freedom: when to use infinity?

I have this question: When performing a certain task under simulated weightlessness, the pulse rate of $42$ astronaut trainees increased on the average by $26.4$ beats per minute with a standard deviation of $4.28$ beats per minute. Construct a two…
SNpn
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Is this method to find mean already discovered?

I am a 10th class student and in our syllabus, we have three methods for finding mean of grouped data: Direct method. Assumed mean method. Step deviation method. Out of these, the Step deviation method is the simplest but still requires a lot of…
Kartik
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mean and std deviation of a population equal?

Hypothetically, if we have a population of size $n$ whose mean and std deviation are equal, I think with some work we have a constraint that the ratio, (Sum of squared points)/(Sum of points$)^2$ $= \frac{(2n-1)}{n^2}$, which gets small quickly as…
daniel
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General question about statistical concept

In parametric statistics, the goal is to estimate the parameter of a population assuming that we know the form of the density of the population. What happens if we do not know the form of the density of the population? In all practical problems, we…
lord12
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Expected value versus mean value

What is the difference between the expected value and mean value of a discrete random variable or discrete uniform distribution?
Mathperson
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Question about posterior distributions and sufficient statistics

1. If $X_1,X_2,\ldots,X_n$ are discrete r.v.'s with joint pmf $f(x_1,\ldots,x_n|\theta)$. Let theta be a discrete random variable with prior pmf $\pi(\theta)$. Let $H(x_1,x_2,\ldots,x_n)$ be a sufficient statistic. Show that…
lord12
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