# Questions tagged [random-variable]

A random variable or stochastic variable is a value that is subject to chance variation (i.e., randomness in a mathematical sense).

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### What is the median of the minimum or maximum of multiple samples?

Suppose I have a variable with a known distribution, and suppose I sample that variable k times and record the minimum. If I repeat this many times, will the median of the minimum converge to a ...
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### Singular values of $A^{-1}$ where $A$ has standard normal entries

Is anything known about behavior of singular values of $A^{-1}$ where $A$ has standard normal entries? Empirically, $k$th singular value appears to decay as $1/k$, is this well-known? colab
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### What do these definitions have to do with random variables?

(This is a full rewrite of the original question I asked. The original was very poorly phrased - I'm hoping this rewrite gets at the central question more directly.) (Take two of the rewrite because I ...
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### Finding a Pivotal quantity

0 I am working on this problem for class, where the setup is the following: Let X be a single observation from the beta(θ,1) pdf. (b) Find a pivotal quantity and use it to set up a CI having the same ...
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### Transformation of a Random Variable

I am working on this problem for class, where the setup is the following: Let X be a single observation from the $beta(\theta,1)$ pdf. (a) Let $Y=-(logX)^{-1}$. Evaluate the confidence coefficient of ...
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### Finding the set for random variable transformations

I'm reading through the book "All of Statistics", and in section 2.12, regarding Transformations of Several Random Variables, the author lists three steps for finding the transformation. I ...
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### Expected value of the product of three random variables

For two dependent random variables we have: $$Cov[X, Y] = E[XY] - E[X]E[Y]$$ So that $E[XY] = E[X]E[Y] + Cov[X, Y]$ In case of three arbitrarily correlated random variables $(X, Y, Z)$, is it possible ...
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### If $X \sim\textrm{ Bin}(100, 0.5),$ then what is the approximate distribution of $(X/5 - 10)^2?$

I am not able to solve this using transformation since binomial does not have a CDF. The question has 4 options, so I tried calculating the expectation of this and then comparing it to the ...
I am reaching out to seek assistance with a probability problem involving random variables. For each $p$ in $[1,\infty)$, consider positive random variables $X_{1,p}, X_{2,p}, \ldots, X_{n,p}$ such ...