Statistical Analysis Stack Exchange
Statistical Analysis Stack Exchange

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).

As opposed to other mathematical variables, a random variable conceptually does not have a single, fixed value (even if unknown); rather, it can take on a set of possible different values, each with an associated probability.

Reference: Wikipedia

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How to generate random categorical data?

Let's say that I have a categorical variable which can take the values A, B, C and D. How can I generate 10000 random data points and control for the frequency of each? For example: A = 10% B = 20% C = 65% D = 5% Any ideas how I can do this?
user333
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Variance of two weighted random variables

Let: Standard deviation of random variable $A =\sigma_{1}=5$ Standard deviation of random variable $B=\sigma_{2}=4$ Then the variance of A+B is: $Var(w_{1}A+w_{2}B)= w_{1}^{2}\sigma_{1}^{2}+w_{2}^{2}\sigma_{2}^{2}…
Sara
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Halving a discrete random variable?

Let $X$ be a discrete random variable taking its values in $\mathbb{N}$. I would like to halve this variable, that is, to find a random variable $Y$ such as: $$X = Y + Y^*$$ where $Y^*$ is an independent copy of $Y$. I am referring to this process…
Joannes Vermorel
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Integral of random variable

I have an integral I need to evaluate that contains a random variable? How would I go about doing something like that. For instance lets say I have a random variable $C$ with PDF $f_C(x)=1/N \; 0\le x\le N$ (Uniform distribution) and I have an…
Twiltie
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Metric spaces and the support of a random variable

Does the use of metric spaces to describe the support of a random variable provide any greater illumination? I ask this after reading about how metrics spaces have been used to unify the mathematical measure theoretic nature of probability and the…
some1
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PDF of function of X

I'm learning about functions of random variables and am trying to work out an example I made up. If $y = \sin(x)$ and $x$ has domain $[0, 4\pi]$, is the following the correct expression for the pdf of $y$: $$\begin{align*} f_Y(y) &=…
Vivek Subramanian
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Is there a verifiable way to generate discrete random variables on the basis of an external event?

Suppose that we want to generate a draw from the following distribution: $P(X=0) = 0.5$ $P(X=1) = 0.5$ There are two constraints though: (a) The draw has to be on the basis of an external event. (b) Related to (a), the draw must be verifiable by a…
user28
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Is that meaningful to compare two random variables?

Currently, I was wondering can we just compare two random variables just like the way we compare two real numbers? Does that make sense? Like for instance, $X$ and $Y$ are two random variables, does $X>Y$ mean something? Or is it plainly nonsense?…
shijing SI
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what exactly does it mean when we say "Let $X_1, X_2 ...$ be iid random variables"

Every now and then I read that phrase and get confused. When we say "Let $X_1, X_2, \dots X_n$ be iid random variables" I thought this meant that we are sampling $X$ random variable n many times for infinitely many times. Let's say we want to know…
MoneyBall
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Probability that random variable B is greater than random variable A

I would like to find the answer to the following question. A casino offers games with one of the following 21 p’s [0; 0.05; 0.10 .... 0.90; 0.95; 1] and one of the following 21 v’s (values) [0; 5; 10 ... 90, 95, 100]. The person taking part in the…
Franz Brentano
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A question on continuous random variable

Let say, I have 2 continuous random variables X1 & X2. Both have same location parameters. Other parameters may be same or may not. Now say, the q1-th quantile of X1 is less than the q1-th quantile of x2. But the q2-th quantile of x1 is more than…
Ron
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Can non-random variables be expressed as random variables with probability 1?

Suppose that $a = 5$. In this case, $a$ is not random since it is always equal to $5$. Can $a$ instead be interpreted as a random variable $X$ such that \begin{equation} p(X=x) = \begin{cases} 1 &\text{if} \quad x = 5 \\ 0…
mhdadk
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What does it mean to multiply 2 random variables that have different sample space?

Here's a problem from Harvard's Stats 110 class: Let $Z \sim N(0,1)$ and let $S$ be a "random sign" independent of $Z$, i.e., $S$ is $1$ with probability $1/2$ and $-1$ with probability $1/2$. Show that $SZ \sim N(0,1)$. Here is the proof, given…
samlaf
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Must a Random variable be Injective Function?

I've recently get to the notion of very basic of statistics. The statistics is trying to assign a "Random Values(mostly in $\Bbb R$)to the given specific event. So the defining of random variable f would be : $f: \frak C \rightarrow \Bbb R$ where…
Daschin
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Mean of Random Process

I have the following question given in Communication Systems by Dr Sanjay Sharma :- "Show that the random process $X(t) = A cos(\omega t + \theta)$ where $\theta$ is a random variable uniformly distributed in range $(0, 2 \pi )$ , is a wide sense…
euler16
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