Exercise · ZW-RANDOM-SAMPLE-009 · ★★★ Advanced
The heights of 3 siblings are called a random sample of the adult population. What goes wrong?
Choose one option.
Show answer
- C. They are not independent: siblings share family and genetics
Explanation
Siblings resemble each other, so the observations are not independent and do not represent the population well. The small size is not the core problem.
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.
\[X_1,\dots,X_n\ \text{independent and identically distributed}\]
More practice problems: random sample
- ZW-RANDOM-SAMPLE-001 A coin with P(heads)=tfrac14 is tossed 3 times independently. What is the probability of the sequen…
- ZW-RANDOM-SAMPLE-002 A fair die is rolled 4 times. What is the probability that all 4 results are even?
- ZW-RANDOM-SAMPLE-003 Which two properties define a random sample X_1,dots,X_n?
- ZW-RANDOM-SAMPLE-004 A variable takes the values 0, 1, 2 with probabilities 0.2,\ 0.5,\ 0.3. In a random sample of size…
- ZW-RANDOM-SAMPLE-005 A coin with P(heads)=0.3 is tossed 4 times independently. What is the probability that all 4 are ta…
- ZW-RANDOM-SAMPLE-006 A random sample of the students of a school is wanted. Which procedure comes closest to that ideal?
- ZW-RANDOM-SAMPLE-007 Two balls are drawn from an urn with 5 red and 5 blue. In which case do the two draws form a random…
- ZW-RANDOM-SAMPLE-008 If X_1,dots,X_n is a random sample, what holds for P(X_1≤ a,\ X_2≤ a)?