Exercise · ZW-RANDOM-SAMPLE-008 · ★★☆ Intermediate
If \(X_1,\dots,X_n\) is a random sample, what holds for \(P(X_1\le a,\ X_2\le a)\)?
Choose one option.
Show answer
- B. \(P(X_1\le a)^2\)
Explanation
By independence the product is \(P(X_1\le a)P(X_2\le a)\), and since they share the distribution it equals \(P(X_1\le a)^2\).
Review the concept: Random sample
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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