I have learned that a Random variable is a mapping from sample space to a real number and is denoted as X, Y ,Z for different functions (random variables). Say, in the case of rolling two dice, X can be defined as random variable that gives the probability of the sum of the face value upon rolling and Y another random variable that gives the probability of the face value being even.
Okay and now as I move on from probability to statistics I see the "Random variables" in the definition of a sample and there it has been denoted as X1, X2, X3, with subscripts denoting the random variable. I am totally confused with the notation and does X1,X2,X3....Xn imply n different random variables ? Can somebody interpret the meaning of the ideology.
Source : - the textbook definition of a sample given in the textbook "Mathematical Statistics with Applications" by Ramachandran:
"A sample is a set of observable random variables X1,X2...,Xn. The number n is called the sample size."