What is the difference between multivariate random variables and sample random variables? 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 ?
 A: 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.
