Exercise · ZW-RANDOM-SAMPLE-004 · ★☆☆ Basic
A variable takes the values 0, 1, 2 with probabilities \(0.2,\ 0.5,\ 0.3\). In a random sample of size 2, what is \(P(X_1=2,\ X_2=0)\)?
Choose one option.
Show answer
- B. \(0.06\)
Explanation
By independence: \(P(X_1=2)\,P(X_2=0)=0.3\cdot0.2=0.06\).
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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