# Tagged Questions

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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### Is the multiple of a Weibull distributed variable also Weibull distributed?

A Weibull distributed variable $X \sim \textrm{Weibull}(\lambda, k)$ has probability density function $f(x):$ f(x;\lambda,k) = \begin{cases} \frac{k}{\lambda}\left(\frac{x}{\...
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### random variable exponential [on hold]

Let the random variable X denote the point (distance) at which either of a motorcyclist’s tyres is destroyed. The probability that the motorcyclist can travel x miles without suffering non-repairable ...
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### Covariance between two random variables with different number of values?

Let's say I have a RV $X$ with values $100$, $200$ and their associated probabilities, and some RV $Y$ with values $35$, $47$ and $862$ with associated probabilities. What does it even mean to find ...
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### Why are we using population symbols ($\sigma^2$, $\mu$, …) instead of sample symbols ($s^2$, $\bar{x}$, …) for Random Variables?

In my Stats course (can't ask prof, it's an online course), we got to random variables and the notation has changed from using $s^2$, $\bar{x}$, etc...to using what we were initially taught are the ...
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### Changing the basis of random variables

Let $X_1$ and $X_2$ be two independent (1-dimensional) random variables and let $Y_1 = f^1(X_1, X_2)$ ($f^1$ is a deterministic function) be a (1-dimensional) random variable too. Question Does ...
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### How to deal with “circular” or “modded” quantities like phases?

I have coefficients $A$ and $\phi$ for data of the form $\sin (A x + \phi)$. The $A$ is fine for all values, but the $\phi$ values I get are always in the interval $[0, 2\pi]$, i.e. they are always ...
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### Method for stochastic data partitioning

I have one task. I have random polynomial like $F(x) = a_0(\omega) + a_1(\omega)x +\cdots+ a_n(\omega)x^n$, where $a_i(\omega)$ is a random variable for each $i = 1, \ldots, n$. Let looks for a ...
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### generated two, specific random variables with a correlation

I would like to know which is the best method to do the following: - generate a random variable $Y$ over $Z_2$ (possibly following a Bernoulli distribution) such that $Y$ has correlation $\rho$ with a ...
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### Problem on convergence of sequence of random variables

Given any sequence of random variables $\{ X_n \}$; how do I show that there exists a sequence of real numbers $\{ \alpha_n \}$, such that $\{ \alpha_n X_n \}$ converges in probability to 0 ?
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### Is it okay to write the square of expectation of a random variable $X$ as $\mathbb{E}^2(X)$?

Is this notation accepted when I write $\text{Var}(X)=\mathbb{E}(X^2)-\mathbb{E}^2(X)$?
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### Probability than empirical mean of one binomial RV smaller than another

Lets suppose I have two binomial random variables: $X \sim B(n_1, p_1)$ and $Y \sim B(n_2, p_2)$. I would like to calculate the probability than the empirical mean of $X$ be smaller than the empirical ...
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### Difference between power of a random variable and product of random variable with itself

In the R package distr there are two infix operators ^ and ...
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### Is the sum of a discrete and a continuous random variable continuous or mixed?

If $X$ is a discrete and $Y$ is a continuous random variable then what can we say about the distribution of $X+Y$? Is it continuous or is it mixed? What about the product $XY$?
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### Treating X as non-random under random sampling

Random sampling allows us to treat values of independent variables that have been sampled as non-random (for the purpose of proving the unbiasedness of OLS estimators). How is this possible? My ...
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### Transformation from skewed to symmetric distribution

Let us consider a positive valued random variable $X$ which is following a positively skewed probability distribution. Is it possible to a get a function $f$ (one-to-one) for which $f(X)$ follow a ...
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### Exemple of real-life non-linear correlation in time series?

I am looking for a dataset of 'real-life' time series that exhibits non-comonotonic / non-countermonotonic dependence. I am not looking for the textbook X^2 correlation, but interesting yet real non-...
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### Difference between (quantitative,qualitative) vs (discrete,continuous)

Could someone please clarify the difference between these seemingly interchangeable groups? (quantitative,qualitative) vs (discrete,continuous). Obviously they are not, but I cannot seem to pinpoint ...
Suppose we have the following random variables $X_1$, $X_2$,....$X_n$,.., that are $iid$ but we dont know what distribution they follow. I know that the sample mean $\bar{X}$ is an unbiased ...