Random sample and random variables

Question

I am new to the statistics and my problem is that i do not understand what a random sample is.

Is it a set of constant numbers, like $X=\{c_{1},c_{2},...,c_{n}\}$.

Is it a set of random variables, with every random variable represents the results of an experiment, like $X=\{X_1,X_2,...,X_n\}$, where $X_i=\{c_{i,1},c_{i,2},...,c_{i,n}\}$ and c(i,j) is the result of an experiment(what i meant to say is every random variable have different sample space but with the same size).

Is it a set of random variables but they all have the same sample space $\Omega$, like $X=\{X_1,X_2,...,X_n\}$, where $X_i=c_i\in\Omega$.

If you can give me an example.

Thank you!

Answer 1

A random sample is when every member of a population has an equal chance of being selected. Example: Let's say Ford produces 500 of a new model of truck. They want to check for defects in the production process. So they pick 10 of the trucks to test. The trucks are numbered 1 to 500. Usually a random number table or random number generator is used to select 10 numbers (which would match to 10 trucks). This is basically the equivalent of drawing names (or numbers) out of a hat.