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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inequality in statistics $P (ω : P (ω) ≤ \alpha) ≤ \alpha.$

We say that a random variable $E (ω)$ is an e-value if $E [E] ≤ 1,$ and we say that a random variable $P (ω)$ is a p-value if for any $\alpha \in [0, 1]$: $P (ω : P (ω) ≤ \alpha) ≤ \alpha.$ Prove that $P = \min \{1, 1/E\}$ is a p-value. The range of…
Jonathen
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Fitting a sinusoidal function to three known points separated by $30$ degrees

I have three data points measured at $-30$, $0$, and $30$ degrees, respectively. I would like to fit these points to a sinusoidal function of the form: $$f(\theta)≈A\sin(\theta + B) + C$$ Is this possible? If so, what would be the best approach? I…
user1799178
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Coefficient of Determination for inverse relationships

I have obtained two data sets which I have already proven to have an inverse relationship. However, can I used coefficient of determination (R^2) to determine the correlation between the two variables? I'm not sure if it can be used for other…
昨晚忘記呼吸
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Unable to find my error in calculation of the minimum net worth of a family needed to be in the Top 1% by using the equation $n t^{c_1} = c_2$

Problem: a) How large does a family's net worth have to be to be in the top $1$ percent in 2019? b) a) How large does a family's net worth have to be to be in the top $2$ percent in 2019? Answer: I will work in units of thousands of dollars. My…
Bob
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Interquartile range

I have grouped data ranges that I need to find the interquartile range for, I think i have found the groups that the upper and lower quartiles are in, but as they are ranged, where do I go from here? Do I find the mid point of each range and then…
Jamie
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Standard error confusion

I am a bit confused by different definitions of the standard error term in statistics that I find. For simplicity I will only refer to the standard error of mean. In one place I find that it's defined as the standard deviation of sample means and in…
Esoog
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Calculate number of bots in tf2

I saw a video a while back on how this game TF2 was getting an influx of bots. The player numbers on Steamcharts are logged for all games, but because of the bots in TF2, the player count is inflated. In a normal game, there are fluctuations in…
James Huang
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Explanation involving moment generating functions, moments and the log-normal distribution

If $Y_1,...,Y_n$ are normal with $\mu$ and $\sigma^2$, and $X_i = e^{Y_i}$, then $X_i$ are log-normal. I want to show that $E(X_i) = e^{\mu+\frac{1}{2}\sigma^2}$. The explanation is that $E(X_i) = E(e^{Y_i}) = M_{Y_i}(1) =…
user952685
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Let $X$ be a random variable with $E[X] > 0$ and $ 0 < E[X^2] < \infty$, prove the following statements holds.

Let $X$ be a random variable with $E[X] > 0$ and $ 0 < E[X^2] < \infty$, prove that $P(X > tE[X]) \geq \frac{(1-t)^2E[X]^2}{E[X^2]}$ for all $0 \leq t \leq 1$. How do I prove this? I first used Markov's inequality and get $P(X > tE[X]) \leq…
user1070420
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LRT and Power for a Normal Distribution

For one observation $Y$ from a normal distribution with variance $1$ and mean $0$ or $2$, consider $H_{0}:\mu=0$ and $H_{1}:\mu=2$. Suppose first that we observe only $Y$. Construct a size $\alpha$ likelihood ratio test. Give explicitly the…
Kirk Fogg
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Understanding the formula for leverage.

I'm reading a stats textbook and it covers the idea of leverage (page 99): $$ h_i = \frac{1}{n}+\frac{(x_i-\bar{x})^2}{\sum_{i'=1}^n{(x_i-\bar{x})^2}}. $$ I understand the second term---squared distance of the $i$-th independent variable from the…
FountainTree
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How to calculate signifiance on an A/B test on revenue

I am having trouble calculating the statistical significance of a split test based on revenue. Most online calculators only look at the number of visitors and the number of conversions, outputting a p-value (and thus measuring the significance). I…
Jeremy
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Expected Value of Exponential Distribution

I want to see if I am doing this right: Let $X_{1},\dots,X_{n}$ denote a random sample from the exponential distribution, with unknown location parameter $\theta$ and scale parameter $\lambda$, whose density is given by $$…
Kirk Fogg
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How is it possible that the best option changes when a hidden variable is taken into account?

If we have two professors teaching the same course course, and last semester of professor A's students, 63 failed and 2037 succeeded while of professor B's students, 16 failed and 784 succeeded, then the success rate of professor A is 97% and the…
Jasper Driessens
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TF2 crithack detection via statistical analysis

This is a idea that I've been thinking about for quite some time, but I'm not good enough at statistics to work out how to do it. Sorry in advance. I don't plan to implement this, but feel free to correct anything I've written about the game that is…
Anamne
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