# 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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### Taking a limit under absolute value

Assume $Z = \mu V + \sigma \sqrt{V}U$, where $V \sim \Gamma(n/2,1/2)$ and $U$ is a sum of dependent standard normal random variables. I'm looking at $\frac{|Z|}{n}$, as $n \to \infty$. My question: is ...
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### Why can a set of random variables be called a sample? [duplicate]

I am trying to understand this slide on sample means. I understand the meaning of the word sample to be a set of individual objects as if grabbing a handful of jellybeans from a packet. Yet in this ...
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### I can't find a way to find the mean of x and the standard deviation of x of this problem [closed]

I can't find a way to find the mean of x and the standard deviation of x in this problem without making an insane amount of calculations. The problem is below. Please help. When planning a party Mr. ...
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### Sum and Multiplication of Two Normal Distributions [duplicate]

I'm not sure about how to go about this question. How do we deal with the variances when the two normal variables are summed?
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### Can a random variable be uncorrelated with its product with a correlated random variable?

I have a random variable $X.$ I want to find a random variable $Y$ such that $Y$ is correlated with $X,$ but $Y$ is not correlated with the product of $X$ and $Y.$ Is it always possible?
1answer
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### How to estimate correlations between products of random variables?

I have three random variables: A, B and C. I know their pairwise correlations. In other words, I know what is correlation between A and B, B and C, and finally, A and C. I also know means of all three ...
2answers
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### Likelihood $L(\theta; \mathbf{y})$: Is $\theta$ a vector of parameters or is it a single parameter?

I have the following definition of likelihood: Let $y_1, \dots, y_n$ be a sample of observations taken on corresponding random variables $Y_1, \dots, Y_n$ whose distribution depends on the parameter(...
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### How are differential equations and stochastic differential equations different?

In the simplest terms, how are differential equations and stochastic differential equations different? As far as I can tell, SDEs are PDEs or ODEs, where the derivative of some function wrt itself is ...
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### Can someone help me understand the random effect parameters in my linear mixed model output?

I have some data for which I modeled in a linear mixed model. I understand everything except the random effect parameters. These variance parameters appear to be bound between -1 and +1. How do I ...
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### If $E[|X_n|] = O(n)$ is $E[|X_n|^2] = O(n^2)$?

Let $X_n$ be a random variable that depends on $n$ and suppose $E[|X_n|] = O(n)$. Then can we say $E[|X_n|^2] = O(n^2)$? If it doesn't hold in general, are there particular interesting cases where it ...
1answer
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### Question about random sample vs support

I got a quick question. Say you have X is random variable X=1 you have sucess X=0 you have failure. And you the following list of number [1,0,0,0,1] So would the list be the support of the random ...
1answer
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### CLT for non iid random variables

Assume $U_k$ are correlated standard normal random variables. Let $R_k := a_k U_k$. I'm looking for CLT of the sum $S_p := \sum_{k=1}^{p}\frac{R_k}{\sqrt{p}}$. Since $U_k$ are correlated, I'm looking ...
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### Sum of correlated squared normals

Assume that $(X_1,X_2)' \sim \mathcal{N}((\mu_1,\mu_2)', \Sigma)$, $j =1,2$, and $Cov(X_1,X_2) = r > 0$. We know that $X_1 + X_2 \sim \mathcal{N}(\mu_1 + \mu_2, \sigma_1^2 + \sigma_2^2 + 2r)$. ...
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### Calculating the sample cumulative distribution function for a Kolmogrov-Simulation test to examine the goodness of fit with given data [duplicate]

I have sample data for 'Times between successive crashes of a computer system' which is for a 6 month period and the data is given in hours. The data in brief is : 1,10,20,30,40,52..... I need to use ...
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### Distribution of $X_1^2 + X_2^2$ and $X_1^2 X_2^2$ for correlated normal r.v

Assume that $X_1, X_2$ are standard normal random variables with $Cov(X_1,X_2)=a$. Then $X_1^2, X_2^2$ are correlated gamma random variables. Are there any known results for the distribution or the ...
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