# Tagged Questions

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 analysis.

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### CLT for continuous functions of random variables

Let $(X_i)$ be a collection of zero mean, unit variance, real valued random variables (I do not assume that they are iid). Let $\mathcal H$ be a separable RKHS with a bounded kernel $k(x,y)$. Suppose ...
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### Sample size given Type I and Type II errors

I have a normal distribution $X \sim N(\mu;0.002)$. We want to test if $\mu=10$. Determine the size of the sample if we want The probability of rejecting the hypothesis $\mu=10$ given that $\mu=10$...
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### Why is this Markov chain's stationary distribution not (1/2, 0, 0, 1/2)?

I have the Markov chain 1, 0, 0, 0 1/2, 0, 1/2, 0 0, 1/2, 0, 1/2 0, 0, 0, 1 I understand how to build the system with which I am supposed to find that ...
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### Exponential smoothing and variance

I have a time series, let's denote it as $X_t$ (a series of prices). We exponentially smooth the data to obtain another time series, an exponential moving average: $EMA_t$. My question is how do I ...
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### Range of a random variable

A set of notes i'm working through gives the following definitions of the range of a random variable and then in addition a variation of the definition. Definition: The range of a random variable is ...
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### Chi Distribution Problems [closed]

I don't really understand how to solve these...could anyone help me out? 1)How to find the expected value of χ2(9) ? 2)We have a point A(x,y,z) in a 3 dimensional space. Each of the coordinates is ...
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### PPK Target Values

I'm assessing specifications for a bunch of different products my company makes and determining whether or not the manufacturing processes are in control. To do this, we are calculating Ppk Values ...
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### existence of some variance over chebyshev's inequality

From the basic knowledge I have, there must exist the variance for some epsilon greater than zero but less than 1 for which the Chebyshev's inequality holds. Now the scénario I have to verify using ...
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### Proof of Chebyshev's inequality for a geometric random variable

I have learnt the Chebyshev's inequality for a continuous case like log-normal and normal distributions and in trying to understand the application I came across the question: For a geometric ...
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### Find the critical value in Tukey's HSD

I'm trying to find the formula for finding the critical values for Tukey's HSD but I can't find any documentation on how to calculate the critical value based on the number of groups the type I error ...
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### multiple linear regression model: scale the dependent variable y by a factor $c ∈ \mathbb{R}, c \neq 0$ [on hold]

In the multiple linear regression model $y = Xβ + u$, if you scale the dependent variable $y$ by a factor $c ∈ \mathbb{R}$, $c \neq 0$, how does the LS estimator $\hat{β}$ change? Does such a change ...