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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Analytical form of a joint PDF of two uniformly distributed random variables

I was wondering if it is possible to write down (closed-form analytically) the joint density function of two uniformly distributed random variables ($X$ and $Y$, each on a closed interval $dX=x_2-x_1$ & $dY=y_2-y_1$) as a function of the correlation…
Mar123
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Calculating future data based previous data

The sales volume of the next month is predicted by the data in the past. The sales volume is changed greatly from month to month, but the annual fluctuation pattern is almost the same every year. Which of the following is the most…
f855a864
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Power of statistical test with uniform random variables

Let $U_i$ be iid and $U_i \approx U(0,1)$. $$\begin{align} H_0: X & \approx \min(U_1,U_2,U_3) \\ H_1: X & \approx \min(U_1,U_2) \end{align}$$ Find power of this test if $\alpha = \frac{1}{8}$. I think that by $H_0$ we have $X \approx F_X(x) =…
Thomas
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Likelihood Function and Derivation

Suppose we have a matrix $V$ of size $p \times n$ where $p \gg n$. We want to factor $V$ into two non-negative matrices $W$ and $H$ where $W$ has size $p \times k$ and $H$ has size $k \times n$. Ultimately we won't get an exact factoring. In other…
Thomas
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Asking for help with statistics. Help explain the method and some tables.

I need to present a paper on Technology Acceptance Model tomorrow morning, which involves some statistical method The non-statistics part of this paper is not hard so I thought I could finish it on time. I did not expect it explained nothing on its…
Ralph B.
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what does drawing samples from a density mean?

I am looking for a formal definition of "drawing samples" (or simply of "samples"), can somebody help me?
peuhp
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Self-study: Maximum Likelihood for a specific normal distribution

This is a self-study. I run into a distribution and I was bored so I wanted to have maximum likelihood estimators (MLE) of the parameters of this specific normal distribution but my mathematics unfortunately got me upside down. Lets say $Y_1,…
ARAT
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prove variance of a RV of 1's and 0's is greater than var of a RV of values on (0,1]

I'm trying to prove that the variance of a RV whose values are discrete 1's or 0's is greater than the variance of a RV who's values are 0's or continuous on the domain (0,1], where any "1" in the Bernoulli RV corresponds to a value on (0,1] in the…
gallamine
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Formulas for proportion charts on map

I try to show pie charts on a map. Each pie chart is a marker for a settlement so the chart size depends on the population. The pie chart sectors contain information about people's nationality. I tried to figure out a right formula to show…
Renya
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Joint probability density of x and y

if the joint probability density of X and Y is given by $f(x,y)=\frac{1}{y}$ for $01/2$ But I am not sure how to set up an integral…
Fernando Martinez
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Theory of hierarchy

In statistical physics we consider a system of a huge number of particles. Each particle on its own is characterized by parameters (like mass or charge) and dynamical quantities (like momentum, energy). Interactions between particles are supposed to…
xaxa
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In Discriminant Analysis (SPSS), why there are F values of the canonical functions?

Recently, I read a paper in which the author uses Discriminant Analysis, here is his words: "The discriminant analysis produced three significant canonical functions (Function 1, F(18, 2130) = 164.81, p<0.0001; Function 2, F(10, 1508) = 85.43,…
Ping Tang
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The probabilities that the independent events

The probabilities that the independent events $A$, $B$, and $C$ will occur are: $\frac34$, $\frac12$, and $\frac14$. What is the probability that at least one of the three events will happen? My solution is $1-$ Pr(intersection of the complements…
Jonarie Ramos Vergara
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Variance of a fair coin toss with standard uniform random variable

Let $X$ be the standard uniform random variable. That is, $X$ has the density $f_X(x) = 1$ for $0 < x < 1$ and $0$ elsewhere. Suppose we toss a fair coin (independently of the value of $X$) and set $Y = \left\{\begin{matrix} X\text{ if the coin…
Schnokeyboy
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Rolling a 15 sided dice

A game of chance involves rolling a 15-sided die once. If a number from 1 to 3 comes up, you win 2 dollars. If the number 4 or 5 comes up, you win 10 dollars. If any other number comes up, you lose. If it costs 4 dollars to play, what is your…
Amanda
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