# 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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### Sum of two i.i.d R.V having singly non-central F distribution

Noncentral F-distribution is used frequently in communication areas. In one of the applications, I need to do a sum of two i.i.d R.V having non-central F-distribution with parameter 1 (d.o.f for ...
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### Calculating the n-th moment of a RV, including negative fractional moments

I am stuck trying to solve the following exercise.. Let $X: \Omega\to [a,b] \subset \mathbb R$ be a uniformly distributed random variable. Compute the n-th moment of $X$, i.e. compute $\mathbb E[X^n]$ ...
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### Computing the expected value of a new Normal Random Variable (transformation)

I have the following exercise to do: Let X be a normally distributed variable with mean μ and variance σ^2, i.e. X∼N(μ,σ^2). Define a new random variable to be Z=X^2−X. Compute the Expected Value of Z ...
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### Dependency and correlation between a random variable and it's square [duplicate]

I have the following question. At first this seemed very silly but after thinking about it, I found my self struggling. Given $X$, a random variable, I should decide if the following sentences are ...
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### What does the parameter s in Sum-of-Gamma mean?

So the sum of gamma, introduced in I-MLE is defined as the following: $$SoG(k,t,s)=\frac{t}{k} \left( \sum^{s}_{i=1} Gamma(1/k,k/i) - \log(s) \right)$$ But what exactly is $s$? It clearly controls the ...
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### What is the distribution of sum of complex Normal R.Vs which are independent?

This may be a trivial question. But I am fairly new to statistics and distributions. I am trying to find analytical solution to sum of complex independendent Gaussian R.Vs following Rician ...
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### correlation: the difference of two correlations is positive, but the correlation of the difference is negative?

There are 3 random variables, $X_1$, $X_2$ and $Y$. We know $$corr(X_2, Y)>corr(X_1, Y)>0$$, but $$corr(X_2 - X_1, Y)<0$$ In other words, $X_2$ is more positively correlated to $Y$ than $X_1$,...
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### Is the median preserved for any strictly monotonic mapping?

Problem Let $X\sim f_X$, where $f_X$ is the probability density function of $X$. Let $g: \mathbb{R} \to \mathbb{R}$ a strictly monotonic (decreasing or increasing) mapping. I aim to prove or disprove: ...
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### How to empirically check a PDF

Intro Let $Y$ be a random variable whose PDF is $p_Y(\cdot)$. Let's say that $Y$ is a function $g(\cdot)$ of another random variable $X$ whose PDF $p_X(\cdot)$ is given. Then, you do your calculation ...
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### Nested or Crossed random effects?

I am conducting an experiment in which participants come twice to the lab to perfom a task. So we have two different experimental sessions, but participants do the same thing in both sessions. The ...
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### How to combine two integrals containing the PDFs of a variable and its linear transform?

Original Post: Suppose we have two random variables $X$ and $Y$ with cumulative distribution functions $F(x)$ and $G(y)$. We know that $Y = aX + b$. I want to compute $Z(x) = F(x) - G(y)$. What I have ...
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### Operations on Random Variables vs Distributions vs Random Samples

What is the difference between i) random variables, ii) distributions of random variables, and iii) random samples? While trying to figure out how to average random samples from various random ...
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Say I have two random variables $A$ and $B$ which may or may not be independent. I also have their $0.95$ quantiles $Q95_A$ and $Q95_B$. What is a valid way to average these densities and obtain valid ...