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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Statistics notations

I'm self teaching myself statistics and got stuck with notations; I'm working with multiple sources and notions seems to differ and confuse me a little, so I decided to write them down first. $ \mu = $ mean of the population $ \sigma = $ std…
Kartopukus
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T-test - pooled variance or not?

Let $X_i$ and $Y_i$ be weight before and after and let's have 5 samples of $x$ and $y$. Calculate a 95% confidence interval for the expected weight loss for the diet method. Thought process: $Z_i = X_i - Y_i \in…
Benjamin Lindqvist
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P-value for lower/upper tailed t-test

I was wondering if the P-value found from a t-table is the same for both lower and upper tailed? For instance let's say I find the P-value in this table: to be 0.05, and I am investigating the lower tail not upper, would my p-value still be 0.05…
jn025
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Exponential Probability Density Function

Find P(x≤6) where f(x)=1/8 e^(-x/8) and e=2.71828 Please show each step, I can't seem to figure this out. Thank you
Ann
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Variance of Estimator / Variance Algebra

I think ive got this correct, but i keep second guessing myself. I have an estimator of an ordered statistic, assuming distributed Uniform[0, 1] The estimator is defined as: $$\hat \theta = X_{(1)} - \frac{1}{n+1} $$ Im solving for the variance of…
James
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Hypothesis testing for coefficients of OLS =0

Suppose that we estimate a standard linear conditional mean model $y=x_1b_1+x_2b_2+e_t$. Then if the null hypothesis $H_0:b_1=0$ is rejected using t-statistic, is $H_0:b_1=b_2=0$ always rejected using Wald statistic? I feel this is logically true,…
atohs
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Markov chain question

I'm stuck with this question saying that, we have a homogeneous MC which is indecomposable and aperiodic, if $\tau$ is the random time of return back to any fixed state. Show that there exist $C>0$ and $q<1$ such that $P(\tau>n) \leq Cq^{n}$. I'm…
Math
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Statistics Review

The class of 2015 at a college, with a graduation rate of 60%, has 250 students. What is the probability that: 1) all the student will graduate in four years? 2) half of the students will graduate in four years? 3) exactly 75% of the students will…
user3254506
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GATE 2014 EE03 question number 27

The mean thickness and variance of silicon steel laminations are 0.2 mm and 0.02 respectively. The varnish insulation is applied on both the sides of the laminations. The mean thickness of one side insulation and its variance are 0.1 mm and 0.01…
R S Selvaraj
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Unbiased Sample variance concern

I have a concern with the unbiased sample variance that I can't seem to understand. $$S^2=\frac{1}{N-1}\sum_{i=0}^{N}(x_i-\bar{x})^2=\frac{\sum_{i=1}^{N}{x^2}_i}{N-1}-\frac{\left(\sum_{i=1}^{N}x_i\right)^2}{N(N-1)}$$ Now I can't understand the right…
George1811
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Does uncorrelated imply covariance is zero?

I know that if covariance is zero then x and y are uncorrelated but does uncorrelated also imply covariance is zero?
user134785
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Normal distribution statistics

please can someone help me do this: The average number of pounds (lbs) of meat a person consumes a year is 218.4. Assume that standard deviation is 25 lbs and the distribution is approximately normal.If a sample of 40 individuals is selected, find…
user150192
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Calculating z-score for non-normal distributions

I am trying to track abnormal values in a dataset over a period of time. Currently, I am using z-scores and the 68-95-99.7 rule for all datasets that are normally distributed. Unfortunately, a small number of these datasets are not normally…
foxygen
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Average separation between discs

The problem is simple: I have discs of diameter $d$ and I am placing them randomly on a plane, area A. I place them at $n$ discs per unit area. What is the average separation of the discs if they are placed randomly? Assume they can't overlap, only…
Jesse
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Confidence Intervals Sample Size

A city planner wishes to determine the proportion of residents who own their home. He wishes to be 95% confident that the estimate is within 2 percentage points of the true percentage. (a) How large should the sample size be? A previous estimate…
sandy
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