This question has confused me a lot in statistics. I think in Statistics, a sample is a pool of data points from the PDF, rather than a single data point, am I correct? In everyday language if you sample something, for example taking a sample from a candy jar, it means just taking a single candy. But in Statistics, it seems that a sample is always like repeating the action of taking the candy 20 times (meaning a sample of size 20). Am I correct?
Also, how do I interpret that sampling in random variable context? Going to that candy jar example, are the candies that I take by repeating the event of taking a candy, each an independent random variable?