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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Probability of histogram bars

Say I collect data that follows a Normal distribution $f(z)$ in a histogram with bins of width $w$. I want to calculate the probability that the number of hits $N_i > N_j$. My naive approach would be to first calculate the probability of finding a…
JorenHeit
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Measuring correlation of a truncated sample

Suppose samples $(X_i,Y_i)$ were drawn from a multinomial distribution $N(\mu_X, \mu_Y, \sigma_X, \sigma_Y)$. The correlation between $X$ and $Y$ can be then estimated as $$\hat{\rho}_{XY}=\frac{1}{N}\sum_{i,j}\frac{(X_i - \mu_X)(Y_i -…
ScarletPumpernickel
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Instrumental Variables and orthogonality conditions

To obtain the method of moment estimate for instrument variables, we use the moment condition $z'\varepsilon=0$ in the exact identified case (number of endogenous variables = number of instruments) or $\hat{x}'\varepsilon=0$ in the overidentified…
ChinG
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Statistical Significance of a Simple Test

Please help me with this basic question on statistics: If a standard brick is dropped on a standard raw chicken egg from 1 meter; the egg breaks. How many times does this dropped-brick-onto-egg need to be repeated to establish statistical…
A J
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Statistical Significance

I'm attempting to compute statistical significance for two data sets. I have the mean and the number of data points, but I don't think I can compute std deviation, because I don't have the individual data points. Under previous teacher, 1,072 tests…
Matt
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Poisson Distribution

I've a question here that I may possibly help with: "Suppose that the number X of errors in an assignment submitted by each student in a certain group is a random variable that has a Poisson Distrubition with parameter Lambda = 4. Suppose also that…
user64219
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Likelihood of large difference in averages

Note that I updated question because initial example grades did not satisfy the overall average that followed from the numbers given in the article. A newspaper artticle in Norway made me curious about this…
ErikN
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Formula to represent 'equality'

I am trying to find the appropriate formula in order to calculate and represent the 'equality' between a set of values. Let me explain with an example: Imagine 3 people speaking on an a TV Show that lasts 45 minutes: Person 1 -> 30 minutes…
gsach
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Expansion of a function with a negative fractional power

How would you expand a moment generating function with a negative fractional power as a power series?? What method would you be able to use?
R.M
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Confidence and proportion

You wish to estimate,with $99\%$ confidence, the proportion of Canadian drivers who want the speed limit raised to $130$ kph. Your estimate must be accurate to within $5\%$. How many drivers must you survey,if your initial estimate of the proportion…
mariah
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Rao-Blackwell Theorem corollary

I have as corollary to the Rao-Blackwell theorem: If a minimum variance unbiased estimator $\hat \theta$ for $\theta$ exists, there is a function $\hat \theta_T$ of the minimal sufficient statistic $T$ for $\theta$ which is a minimum variance…
user152440
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statistics , two different results related in their standard deviation

I have a question I don't know how to think about it. We have a sample of $25$ people, $16$ of them smoke and $9$ don't. The average capacity of their lungs in smokers is $103$ and in non-smokers is $95$ and the standard deviation of all people in…
sinod
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Unbiased estimators for binomial distributed variable

I'm having trouble determining whether the estimator beneath is unbiased or not. First some info: $x_i \sim binom(n_i,p)$ I have a sample of $x_1,x_2,x_3,x_4$ so $n=4$ I want to find out if the…
Kristian
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Confidence Interval Question - Confused on Approaching the Problem

My question is almost exactly the same as another one here on math stack exchange, but it isn't as explanatory as I'd like it to be with some parts. I was unsure of whether or not it'd be "okay" to repost the question, especially since the other one…
Super Rhinocerus
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Direction of Study Suggestion

I'm not sure if this belongs in stats or here, or why stats would be considered different to math. During my self-study of biochemistry and medicine, I notice that a vast range of published studies are flawed and irreproducible, leading to…
user4779
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