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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Population Cumulative Distribution Function with Simple Random Sampling

Link to textbook example: http://puu.sh/CEgk2/b5d08453fb.png Context to Example 5.4.1: http://puu.sh/CEgmt/c6390a8bba.png Hi, I was reading up on my textbook readings for my intro to stats class, and I got confused over an example that was provided…
Donald Mayer
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Stuck at hypothesis testing assignment

So I have this assignment in statistics that states the following: We need to either accept or throw away a big package of processors. Because of quality control we take take a sample of 200 processors and find 24 that are not working. The maker of…
David Mason
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Compute the Mean Squared Error of $$

The famous biologist Henk de Rijn has come up with a skill test for chimpanzees. We assume that each chimpanzee has a probability $$ to pass the test, independent from previous attempts and from other monkeys. Let $_$ be the number of attempts…
Luke Marci
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Use the Central Limit Theorem to deduce that if $λ$ is large, then $X$ approximately has a normal distribution.

The time instants of incoming requests at a data server can be modelled with a Poisson process. Let $X$ be the number of requests in one hour and let $λ$ be the intensity (requests per hour) of the Poisson process. - Use the Central Limit…
TFAE
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A manufacturer of space shuttle light bulbs claims that the defect rate of the bulbs is $0.1\%$.

A manufacturer of space shuttle light bulbs claims that the defect rate of the bulbs is $0.1\%$. You suspect the defect rate is actually higher, so you have checked $1000$ identical light bulbs from this manufacturer and found out that 3 of them…
TFAE
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Coefficient of determination, why?

I mean it is written in a book "Statistics for Management and Economics", that coefficient of determination is coefficient of correlation squared. Well, am I the only one to whom this is surprising fact as he expected something more clear or…
nikola
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Use an appropriate statistical test to test the manufacturer’s claim at significance level $α=0.05$.

The manufacturer of the resistors claims that the expected maximum power at which the resistor fails is $0.25$. You suspect this threshold is lower and therefore decide to measure the current and resistance at which the resistor breaks down. …
TFAE
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How to find which percentile is a value in a skewed normal distribution

I have a skewed normal distribution for which I know the average, standard deviation, skewness & kurtosis (which is different from zero). Given a number $X,$ how can estimate which percentile corresponds to that value? (I'm ok with getting an…
Nisalon
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Modeling a yes/no event

I was wondering what kind of distribution applies to a variable that can have one of two outcomes (say yes or no) but the probability of any of these outcomes is completely random and cannot he determined ? Example: I am stopping 10,000 people on…
Jay Kay
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How do you calculate IQR (interquartile range)?

I have the following data (ordered): $$0, 1, 1, 2, 3, 4, 4, 7, 9, 23.$$ As far as I know, $Q_1 \text{(median of the upper half)} = 1$; $Q_3 \text{(median of the lower half)} = 7$; Therefore, $\text{IQR} = Q_3-Q_1 = 6$. But when I boxplot this simple…
ToNoY
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Bootstrap-related issue

Say I re-sample $N$ items with replacement from a numbered item sample of size $N$. What is the average number of data items that are not selected in each such sampling?
Omri
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More efficient estimator?

I have this kind of problem: The market share $Z$ of a company is estimated in two independent survey polls. The sample sizes are $n_1=500$ and $n_2=2000$ with corresponding observed shares $p_1$ and $p_2$, respectively. These two results are to be…
Dennis
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Help with Likelihood Function Notation in Logistic Regression

Can someone please help me understand below notation I encountered while studying logistic regression? I am pretty sure I lack the mathematical maturity but would like to give it a try. $l(\beta_0,\beta_1) = \prod_{i:y_{i=1}} p(x_i)…
DoLare
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What's the meaning of multiplicative errors and additive errors?

Such skewed, thick-tailed data suggest a model with multiplicative errors instead of additive errors. A standard solution is to transform the dependent variable by taking the natural logarithm. Can anyone explain multiplicative errors and additive…
Yao Zhao
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How to calculate statistical "difference" of two samples in 0-100 range?

There are two groups of people, target and neutral There are two group of events X and others We're making assumption that people from target group react on event X very different to others. We have some sets of reaction numeric values on different…
cnd
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