# Questions tagged [random-variables]

Questions about maps from a probability space to a measure space which are measurable.

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• 193
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### k-independent hash functions vs. orthogonal arrays

In some randomised algorithms, such as Alon-Matias-Szegedy (AMS) algorithm, two different strategies are used for the generation of a family of random numbers with some special correlation properties: ...
• 1,181
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### Show that $XY$ is absolutely continuous and determine its density

If $X$ and $Y$ and absolutely continuous and independent random variables, how to show that $XY$ is also absolutely continuous and what is its density? I know that $X$ and $Y$ are absolutely ...
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### Median of Mixed Random Variable [closed]

I have the following CDF $$F_X(x) = \begin{cases} 0 & x < 0 \\ 1 - p e^{-x} & x \geq 0 \end{cases}$$ I found $\mathcal{X} = \{ 0\} \hspace{0.1cm} \cup (0,\infty)$ with $P(X = 0) = 1-p$ ...
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• 281
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### Uniform distribution problem involving two buses

I am trying to solve the following problem: A bus on line A arrives at a bus station every 4 minutes and a bus on line B every 6 minutes. The time interval between an arrival of a bus for line A and a ...
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### Understanding the use of Indicator function

in my research work I came across following expression: $A = \mathbb{P}[X\geq \tau_s, D\leq \frac{c}{2}(T_c-\frac{cT_c}{2B_s}), Y\geq \tau_c]$---(1) where $\mathbb{P}$ denotes probability, $X,Y$ are ...
• 183
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### An upperbound for the variance of mean estimator in higher dimensions

I am trying to learn from the paper [paper] http://proceedings.mlr.press/v139/karimireddy21a/karimireddy21a.pdf [proofs] http://proceedings.mlr.press/v139/karimireddy21a/karimireddy21a-supp.pdf , ...
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1 vote
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### GLMs where response variable is calculated from multiple data points in a time series?

Hopefully this isn't too broad of a topic: I'm a student research assistant working with matched gene expression counts data in a time series. As a simplified example, say I have two sets of time ...
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### Probability of i.i.d. uninform random variables assuming a particular ordering.

I'm doing the following exercise. Let $X_0, X_1, X_2, . . . , X_k$ be uniformly and independently distributed on [0, 1]. Declare that the $j^\text{th}$ event succeeds if and only if $X_j < X_0$. ...
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### Convergence in distribution of random variables with symmetric distribution

I found the following question in the probability course materials: let $(X_n)_{n\geq 1}$ be i.i.d. random variables with symmetric distributions such that $\sigma^2=\mathbb{E}[X_1^2]<\infty$. ...
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1 vote
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### Proof of Polynomial Behavior in Sequence of Random Variables

Problem statement: Let $X_0, \xi_{i, j}, \epsilon_k$ (i, j, k ∈ N) be independent, non-negative integer random variables. Suppose that $\xi_{i, j}$ (i, j ∈ N) have the same distribution, $\epsilon_k$ (...
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### Distribution of difference of two random variables

The problem is following: Suppose we have a line segment with a length $L$ and we randomly choose (with uniform distribution) $n$ points on this segment, so we divide the main line segment into $n+1$ ...
1 vote
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### Calculate expected value of a function of IID samples

Suppose $X$ is a random variable and $E[X] = \mu$. We define random variable $T$ that for every IID sample $S = \{x_1,..., x_n\}$, then $T(S) = \frac{1 + \sum\limits_1^n x_i}{n}$. Although it is ...
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### Expectation and variance of Y

Let $X$ be an exponential random variable with mean $1$. Let $Y$ be a uniform random variable over the interval $(0,X)$. We were asked to calculate the mean and variance of $Y$. The mean of $Y$ is ...
1 vote
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### Expected rank of a random binary matrix with Bernoulli probability p?

Let $M \in \mathbb{R}^{m,n}$. The entries are in {$0, 1$} (with the value $1$ having probability $p$, and the value $0$ having probability $(1-p)$). What is the expected rank of $M$? Follow-up: how ...
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