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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Finding mean and variance through mean and variance of subsets

Suppose I have a big subset of smaller subsets where each small subset contains x amount of numbers. How would I go about finding the mean and variance of the larger subset through the mean and variance of fragments of the smaller subsets? For…
Omrii
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Testing whether forecasting models differ significantly in their forecasts

I am not finding my question on here which I sort of find it hard to believe unless I am simply on the wrong stack board. If it is on this board, kindly direct me and I will be grateful. Otherwise, I have two models used to forecasting the same data…
Sven
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Probability of picking a complete set of x items from an indefinitely large field after y tries

I'm looking for an equation that will help me calculate probabilities for a project at work. I've been Googling and reading posts here trying to figure out what I need but my unskilled brain is running into roadblocks. I hope that you can point me…
Jon Stanley
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Unbiased estimator of variance from one data point

Let $X_1,...,X_n\sim\mathcal{N}(0,\sigma^2)$. I know that the sample variance $$\hat{\sigma}^2=\frac{1}{n-1}\sum_{i=0}^{n}X_{i}^2$$ of this data is the UMVUE for $\sigma^2$. But what if we have only a single data point? $\hat{\sigma}^2$ is not…
Theo Walker
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Is it possible for some results to be "more" statistically significant than others provided they both have p values less than 0.05?

Say you have two sets, and the mean of one is higher than the other. A two-sample t test yields a result of p = 0.01, indicating a significant difference in means. Another pair of sets also have different means, but a two-sample t test yields a…
Jamerson2
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How to interpret a two-sided graph?

What does the "right" Y-axis represent? Taken from here: https://istheservicedown.co.uk/status/virgin-media/2654675-bristol-bristol-england-united-kingdom
nz_21
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Significance test for ratio

I have that a certain action is performed by $N_1$ unique users in a total of $M_1$ times in the control group, and by $N_2$ unique users in a total of $M_2$ times in the treatment group. I want to calculate if the average number of actions…
ava
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Computing the contribution of individuals to a distribution's equity

I am looking for a function that would determine the contribution of each individual relatively to the non-dispersion (equity) of a distribution. I have a distribution of incomes X (which, letting aside the details, are determined individually…
rchaput
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Please explain how to derive the PGF of a 6 sided dice

I understand the PGF is $$ P(s) = \frac{s}{6} \frac{1-s^6}{1-s} $$ Can someone explain all the steps to get there
Jimmy
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Calculating population size at any future time

If current population size is $P$ and average life-time of any member is $L$. Any pair of member of the population is allowed to have $C$ children on an average. They can have children between the age of $A$ to $B$.Then how can I tell population…
Pratik Deoghare
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Predicting the average number of transitions given a frequency and a set size?

Say I wanted to predict the number of Software Engineers in a given year that change their job. The total number of Software Engineers in a given market is readily available (4.4 million in the US), as are retention rates for companies…
Abraham P
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An exact and an approximate confidence interval for a Poisson distribution

$X_{1}, ..., X_{10}$ ~ $Pois(\theta)$ Observations: $x_{1} = x_{3} = x_{6} = x_{8} = x_{9} = 0$; $x_{2} = x_{5} = x_{10} = 1$; $x_{4} = 2$; $x_{7} = 3$. I want to determine an exact (numerical) and an approximate (numerical) confidence interval for…
Laura van Leuven
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Is there a way to rate how close data is to being sinusoidal?

I am looking for a mathematical method of determining how relatively close a data set is, to fitting a generic sine wave (in other words, $\sin(x)$). In my mind, this would be something like an R squared value for a linear regression, except for a…
Snoop
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Finding the MLE of a multinomial distribution (uneven probabilities)

I am trying to simulate loaded die where the face probabilities are: $$ p_1=p_2=p_3=p_4=1/6+\theta\text{ and }p_5=p_6=1/6-2\theta $$ And so using the multinomial distribution I have: $$ \binom{n}{x_i}\prod_{i=1}^6 p_i^{\displaystyle…
user2331828
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If $X$ and $Y$ are independent random variables, are $X^2$ and $Y^2$ also independent?

If $X$ and $Y$ are independent random variables, are $X^2$ and $Y^2$ also independent? Can this be proven?
mathissfun
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