# 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.

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Scenario ...
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### Curve Fitting Problem

Find best values of a and b if y = ax + b log x is the curve which represents most closely the observed values given below : X: 2, 3, 4, 5, 6 Y: 3.74, 5.99, 7.47, 8.92, 9.86
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### How to show the expectation of gradient estimate is unbiased for least square problem?

Suppose we are given $m$ points $\{a_1, \cdots, a_m\}$ where $a_i \in \mathbb{R}^n$, and the corresponding target values are $\{b_1, \cdots, b_m\}$ where $b_j \in \mathbb{R}$, and we want to solve the ...
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### Testing significance of patterns of results

I'm a high school English teacher conducting an independent study, and I'm a total novice to statistical analysis, so please forgive me if I mischaracterize anything. I have gathered pretest and ...
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### Implication of Chebyshev's inequality

Is it correct that Chebyshev's inequality for a random variable $X$ implies that \begin{align*} P(|X|>\delta) \leq \frac{E[X^k]}{\delta^k} \quad \text{for } k=2,4,\dots \text{ and } \delta >0 \...
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### is crosscorrelation function with 0 lag the same as correlation between the change at each time step?

If I have two time series, $\vec{x} = [x(t_1), x(t_2), \dots]$ and $\vec{y} = [y(t_1), y(t_2), \dots]$, and I compute the crosscorrelation function on these two vectors with a time lag of $0$, is this ...
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### I have a jar with N unique balls. If I draw N random balls with replacement, what is the most likely number of duplicate draws?

I have a jar with N unique balls. If I draw out N random balls with replacement, how many duplicate draws am I likely to have seen when I'm done? I.e., what is the most likely number of times that I ...
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### Law of Kolmogorov-Smirnov statistic

Do you have a easy proof of the fast that the Kolmogorov-Smirnov statistic law is continuous ? Because I don't know anything about Brownian motion. The statistic is defined here. Thanks and regards....
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### Mixture prior of waiting times

Consider there are two equally trustworthy experts, each of them has a belief of the waiting times of a event. Expert A says it's between 5-10 minutes while B says 0-25 minutes. I'm wondering how to ...
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### Developing a model to approximate an unknown score from known scores

Apologies if this would be better suited elsewhere, this is the SE I was recommended. I can delete / move if needed. The target is to approximate a hidden rank in a game (Dota 2 if anyone is ...
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### Stuck on probability/statistics question

EDIT: Post as been edited to address relevant questions raised in comments. I'm new to the site and I'm stuck on a probability question. I don't think it's trivial, certainly not to me, as I am ...
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### Problem Interpreting histogram

I am reading Understandable statistics. In the second chapter, example 2, the author shows the following histogram: The author then proceed to interpret the histogram as follows: About 40% of the ...
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### Does Causation imply dependency in the Euler scheme discretization for SDEs?

My question may sound stupid but I have a confusion concerning the following statement: Assume we have n-observations $(X_0,\dots,X_n)$ that are coming from a discretization of an SDE using the ...
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### Accuracy of estimation of the variance

Consider $N$ i.i.d. samples $x_1, \dots, x_N$ from an unknown discrete distribution on $\{0,\dots, n\}$. We know that $$\frac{1}{N-1} \sum_{i = 1}^N (x_i - m)^2$$ where $m$ is the sample mean, is an ...
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### Infinite monkey theorem independent of number of monkeys

I was just thinking about the infinite monkey theorem and arrived at a creepy conclussion. Let's begin with the probability that one monkey types a set of $N$ letters with a chosen order, which is ...
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### Standard Error and Standard Deviations

How it s possible to calculate standard error for single sample, While standard error is defined as variance in different sample means?
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### Standard Error calculation [closed]

How many standard errors around the hypothesized value should we use to be 98 percent certain that we accept the hypothesis when it is true?
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### AP Stats questions on significance tests

A company produces millions of 1-pound packages of bacon every week. Company specifications allow for no more than 3 percent of the 1-pound packages to be underweight. To investigate compliance with ...
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### UMVUE for a $NB(k,p)$ with $g(p)=p^k$

I am prepping for an exam and this is one of the questions the professor handed to help us prepare. $$X\sim NB(k,p)$$ where $k$ is the number of successes. Find the UMVUE of $g(p)=p^k$ if it exists....