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.
37,743 questions
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Finding the homogeneous polynomial associated with a symmetric tensor
Consider the order $3$, rank $2$ tensor
$$
T = 2e_1^{\otimes 3} + 5(e_1 \otimes e_2^{\otimes 2}) \in \operatorname{Sym}^3(\mathbb{R}^2)
$$
This is rank $2$ in the sense that it is written as a sum of $...
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If a biased coin is flipped once and lands heads, what is the most likely number of heads in 100 future flips? [migrated]
If it is assumed that all possible probabilities of landing heads are equally likely, then the prior probability density of the probability of heads x is q(x) = 1. Bayes’ rule and the binomial ...
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Consistency of Covariance Matrix Estimator in Elementwise Max Norm
Let $X_1,X_2,\dots,X_n$ be iid random vectors in $\mathbb R^d$ with covariance matrix $\Sigma$. I want to show that $$\hat\Sigma := \frac{1}{n-1}\sum_{k=1}^n(X_k - \overline X_n)(X_k - \overline X_n)^\...
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The sum of sub-exponential random variables are sub-exponential.
We will say that a zero-mean random variable $X$ is $(\nu, \alpha)$ sub-exponential if for all $\left|\lambda\right|<\frac{1}{\alpha}$, $\mathbb{E}(e^{\lambda X}) \leq e^{\frac{\lambda^2 \nu^2}{2}}$...
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What is the benefit of the force of mortality over PDF in lifetime analysis
What is the benefit of using the force of mortality $μ_x$ instead of the Probability Distribution Function $f_x(t)$ of a lifetime random variable $T_x$?
I understand that if I have the continuous ...
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In logreg, why do we work with probabilities instead of just using a continous value?
In logistic regression, is there a FUNDAMENTAL reason why I map a continuous value to a probability? Couldn't I simply define a decision threshold from a continuous value? What is the mathematical ...
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Clarification on Possibility of Full House from Deck of Cards [closed]
Why is it incorrect to approach the problem like so, relying on multiplication rule:
For the 3 of a kind
Choose any card at random: 52 choices (52). Once that's locked in, there are 3 choices (3) to ...
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Effect in Quantifying the Separation of Two Distribution When Both Multiplied By a Constant. [closed]
I am working with two histograms, and using the following quantity to quantify the "Overlap-ness" of them:
\begin{equation*}
O = \sum_i\frac{\sqrt{f_i \cdot g_i}}{\sqrt{\sum f \cdot \sum ...
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How to prove $E[X \mid \text{first trial failure}] = 1 + E[X]$ usign memoryless property in geometric distribution?
first of all I wanted to say I haven't red statistics in a proper order, I'm preparing for an olympiad, so pardon me if it's too obvious. The main defination of memoryless property as I know is:
$P(X&...
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Explanation of polling on a simple example
Let's say there are $n$ voters who are going to vote to one of two parties A and B. We want to estimate in advance what party is going to win, so we poll some $k\ll n$ citizens at random. If party A ...
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What is the probability that the second half is equal to the first half? [closed]
There is a jar full of $n$ balls with $k$ different colors ($n>k>1$). We know nothing about the distribution of colors in the jar.
We take out some $n/2$ balls at random, and record their colors ...
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Probability question about coin tossing
Ann and Jim are about to play a game by taking turns at tossing a fair coin, starting with Jim. The first person to get heads twice in a row will win. (For example, Ann will win if the sequence (...
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Convergence in distribution of a kernel average.
Let $\{X_i\}_{i=1}^n$ be a sample of i.i.d. random variables with compact support $[0,1]$, $H$ be a symmetric kernel around 0, that integrates one, with compact support $[-1,1]$, and $h_n$ a function ...
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Non linear relationship [closed]
Are their tools that can analyze the relationship raw seeds and their corresponding normalized values which have a non linear relationship between the independent and dependent variable
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Computing rate statistics from time intervals
Imagine that you observe events occurring at random times. More precisely, the time intervals between events are IID and drawn from the distribution described by the p.d.f.
\begin{align}
\rho(t;\tau,...
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