Exercise · ZW-RANDOM-SAMPLE-010 · ★★★ Advanced
If \(X_1\) and \(X_2\) form a random sample of a discrete variable, which statement is true?
Choose one option.
A \(X_1=X_2\) always B \(X_1\) and \(X_2\) can take different values, but they have the same distribution C \(X_1\) determines \(X_2\) D \(X_1\) and \(X_2\) have different distributions Show answer B. \(X_1\) and \(X_2\) can take different values, but they have the same distribution← Back to the question
Explanation Identically distributed does not mean equal: each is a new observation with its own value, and they only share the probability law.
A random sample of size \(n\) is a set of \(n\) independent random variables \(X_i\), all with the same distribution, that represent \(n\) observations from a population.
\[X_1,\dots,X_n\ \text{independent and identically distributed}\]
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