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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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Statistics Binomial Formula

Jack tosses a fair coin 6 times. Then Jill tosses the same coin 9 times. Write out an expression for the chance that "Jack gets 2 heads and Jill gets 4 heads." I know that you use the binomial formula to get the chances for each but do you then…
user222700
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Find moment generating function

I want to find the moment generating function $M(t)$ for distribution $$ f(x) =e^{-(ax)^{2}}*(1-e^{-(ax)^{2}})^{b-1}*[-log(1-e^{-(ax)^{2}})]^{r-1} $$ $$ M(t):=E(tX) = \int_0^\infty e^{tx}*f(x)dx \,. $$ But I have a problem.
Mundher
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Smallest order statistics

Suppose $X_1$ has exponential distribution with mean $\frac{1}{\theta}$ and $X_2,\ldots,X_n$ have exponential distribution with mean $\frac{2}{\theta}$. also suppose $X_1,X_2,\ldots,X_n$ are independent.how likely that $X_1$ be smallest order…
hadisanji
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statistics conjecture

A engineer conjectures that the population mean of a certain component parts is 5.0 millimeters. An experiment is conducted in which 100 parts produced by the process are selected randomly and the diameter measured on each. It is known that the…
vvavepacket
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How to prove P(A ∩ B ∩ C) = P(A|B ∩ C)P(B|C)P(C)?

How to prove P(A∩B∩C) = P(A|B∩C)P(B|C)P(C)? I've tried to approach this a couple times, but always end up getting stuck :( Any help is appreciated! :)
Maria Sanchez
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Finding an unbiased estimator for $\mu^2$

I'm currently studying my first course in statistics. I am going through some question and have come across one that has stumped me. The question is as follows: Suppose $\bar{X}_1, \ldots, \bar{X}_n$ are $n$ identically distributed independent…
wonggr
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Why is variance defined as the expected value of difference squared?

As I understand it, variance of a random variable is defined as follows: \begin{equation} \text{Var}(X) = \text{E}[(X-\mu)^2] \end{equation} $X-\mu$ is obviously the difference between the value of the random variable and the expected value of the…
Stan Shunpike
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Calculate Probability Given Probability Generating Function

I've come across a statistics problem that I can't seem to figure out how to solve: "A certain discrete random variable has probability generating function: $$ \pi_x(q) = \dfrac{1}{3}\dfrac{2+q}{2-q} $$ Compute p(x) for x = 0,1,2,3,4,5. (Hint:…
Robert
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Point estimation vs hypothesis testing and interval estimation

Can someone explain what are point estimators good for? Hypothesis tests and interval estimations give a fuzzy answer in terms of something sort of like a probability of the value being in some interval. In applied statistics why would you look at a…
user782220
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Maximum Likelihood Estimator of scaled beta

I want to find the MLE of $X = \theta{Y}$, where $\theta > 0$ and $Y \sim \mathrm{Beta}(2,1)$. The density for $X$ is given by $$f_{\theta}(x) = \frac{2x}{\theta^{2}}$$ on $[0,\theta]$. It has been a bit problematic finding the MLE here (for fixed…
forgetfulF
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Help reading a scatterplot

In reading the following scatterplot Would it be correct to say there is a strong positive linear relationship between the two axis? If not, could you please explain why? Also is it correct to consider the ringed point as outlier?
ZeroCool
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Skewness of a difference of random variables?

In this article( http://www.diva-portal.org/smash/get/diva2:302313/FULLTEXT01.pdf )page 28 explains how to derive the skewness of a sum of random variables; I haven't been able to derive this expression in case of dealing with a difference of random…
user3070616
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How do I compare student pre-test scores with post-test scores to evaluate whether or not they "learned"?

We need to track student advancement in a topic based on pre and post test scores. That is, we give a pre-test on day 1 of class, then on the last day we give the exact same test, renamed as a post-test. Somehow we have to take the first score and…
Michael
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How much data do I need to gather?

I'm studying a manufacturing process that produces widgets, with a number of machines that breakdown or jam occasionally. I want to figure out how many hours of studying I need to do, in order to be confident in knowing what the biggest causes of…
Sam
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