# What is the difference between multivariate random variables and sample random variables? [closed]

Multivariate random variables consists of more than one random variable which may be independent , eg. Height , weight , age can be called three random variables and we can write their joint distribution .These can be represented by $$X_1,X_2,...,X_n$$. But when I was reading random sample and estimation topic , I came across random sample variables $$X_1,X_2,...,X_n$$. Are they same as above or for eg. they denote same random variable height for different samples from ?

## closed as unclear what you're asking by user158565, Michael Chernick, mdewey, Robert Long, Jeremy MilesApr 13 at 1:49

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What you are referring to as "multivariate random variables" are usually called random vectors,$$^\dagger$$ and yes, they are just vectors of individual (scalar) random variables. (The individual random variables that are the elements of the random vector can be independent or dependent; for the purposes of classifying the whole as a random vector, it doesn't matter which.)
A random sample of more than one random variable consists of multiple random variables, so it can also be expressed as a single random vector $$\mathbf{X} = (X_1,...,X_n)$$. There are cases where each individual sample point is a scalar random variable, and the overall sample is a random vector. However, in the case you describe (where there are three measurements for each individual), it sounds like each individual data point would be a three-element random vector, so the overall sample would probably be represented as an $$n \times 3$$ matrix, with rows corresponding to different people, and columns corresponding to the measured variables (height, weight, age).
$$^\dagger$$ We generally refer to "random vectors" if we have a finite number of scalar random variables, or a "random sequence" if we have an infinite sequence of them.