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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How is the mean represented in boxplots

How is the mean represented in boxplots? In the image below weather situation 3 shows outliers pulling the mean down and so I reasoned that situation 4 would have a higher mean than the rest because the median has a higher Humidity than situation 1…
sgoodman
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which statistic test should I use for this question?

there is a question like this: Two producers produce a cream with hydrating ingredient. According to the table state, whether the amount of the ingredient is significantly different or not. Use the level of significance 0.05 and assume that data are…
Sina M
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75th percentile of $e^x$

Let $f(x) = e^x$ on the interval $[0,2]$ and $0$ everywhere else. Calculate the 75th percentile of $f(x)$. Attempt So normally I would take the integral from $\int_{- \infty }^{x} f(x)dx$, equal it to $0.75$ and solve for $x$. But $f(x)$ only exists…
Nicco
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Statistics Question MME and MLE

I have been attempting this question for a while and whenever I get to the standard error question of part (a) I keep getting 0. Ok so ai) $$\ E(X)= 3-2\theta $$ $$\ Var(X) = 2\theta -2\theta^2 $$ for aii) I found my MME by equating first…
Mathman
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Variance, mean and median

Is it possible to find an example of two samples each of size 5 which have equal mean and equal variance but distinct median? I thought about this for a while but have not been successful in coming up with such an example, so I believe the answer Is…
Stiven G
  • 535
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Proof related to Chebychev's inequality

I need to prove that in a set of $N$ data $x_1, x_2, \ldots, x_n$, for all $i$ between 1 and $N$, we have $$\mu-\sigma \sqrt N \leq x_i \leq \mu+\sigma \sqrt N$$ where $\mu$ is the average and $\sigma$ the standard deviation. I know I need to use…
Justin D.
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Bias of Estimator with square root of a sum of squared random variables

Got a distribution of $f_X(x;\theta) = (x/\theta^2) \exp(-x^2/2\theta^2)$ for $x \ge 0$ where the MLE is calculated as $\theta_{MLE} = \sqrt{(\sum_{i=1}^{n}x^2_i)/2n}$ So now need to find if it's unbiased by taking the expected value of the…
JakeM
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Any higher mathematical relationship between these survival analysis entities?

For part of some software documentation, I created this image of the relationships between survival analysis entities: survival, CDF, PDF, hazard and cumulative hazard (see image below). There is an obvious horizontal "symmetry" in the image. Is…
Cam.Davidson.Pilon
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Need some help figuring out $E(X^2)$

This is my first question and I hate making this a new question, as I found an answer to a similar question, but it's not quite clear and I don't have enough rep to leave a comment asking for more info. So I got quite stumped trying to figure out…
Kaelus Von Sestiaf
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Theoretical limit on Random Forest performance

If I run a Random Forest on a set of data and get an accuracy of let's say 85% and I want to produce better results, I could just increase the amount of decision trees I use. Lets say I Increase the amount of trees I use and now I get an accuracy of…
GMC2
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Poisson distribution normal approximation

6.4.18. An experimenter takes a sample of size 1 from the Poisson probability model, pX (k) = e−λλk/k!, k = 0, 1, 2, . . . , and wishes to test H0: λ=6 versus H1:λ<6 by rejecting H0 if k ≤2. (a) Calculate the probability of committing a Type…
Jelizabeth
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Can we join CDF and Survival function in Copula

Can we join CDF(cumulative density function) and Survival function like this in copula construction $$ H\left(x_1,x_2,x_3\right)=Pr\left(X_1x_2,X_3
SAAN
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Uniform $(-1,1)$ distribution

Let $X$ and $Y$ be independent with uniform $(-1,1)$ distribution. Please help in finding: a) $P(X^2+Y^2 \leq r^2)$ b) The CDF of $R^2 = X^2 + Y^2$ c) The density of $R^2$ All I tried was breaking it down into cases, for part a we have 2 cases,…
mary
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How to get the sample number?

I have this statement: The weights of a school are distributed in a normal way $\sim N(85, > 8)$ If a sampling is done. what should be the size of this sample, so that the probability of the mean of this sample is less than $87$, is …
ESCM
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Median of 2 sets and median of the sum of the 2 sets

Suppose I have N individuals (N is odd for convenience). Associated with these individuals, two sets (S1 and S2) which contain integer numbers. E.g. S1 is the salary/hour and S2 is the bonus/hour: Individuals = {A,B,C,D,E} S1 = {A=9; B=11, C=13;…
pchat12
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