Exercise · ZW-RANDOM-SAMPLE-007 · ★★☆ Intermediate
Two balls are drawn from an urn with 5 red and 5 blue. In which case do the two draws form a random sample ?
Choose one option.
A Without replacement, because the urn empties B Always, however they are drawn C Never, because the urn is finite D With replacement, because the same experiment is repeated Show answer D. With replacement, because the same experiment is repeated← Back to the question
Explanation With replacement each draw has the same distribution and does not depend on the previous one. Without replacement the first ball changes the probabilities of the second.
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-008 If X_1,dots,X_n is a random sample, what holds for P(X_1≤ a,\ X_2≤ a)?ZW-RANDOM-SAMPLE-009 The heights of 3 siblings are called a random sample of the adult population. What goes wrong?