Pairwise Independence \(\neq\) Mutual Independence
Discrete Mathematics
Level
2
Let \(X\) and \(Y\) be random variables describing independent tosses of a fair coin. Let \(Z\) be the random variable that equals \(1\) if both \(X\) and \(Y\) land heads and that equals 0 otherwise.
How many of the following statements are true?
- The collection of random variables \(\{X, Y\}\) is independent.
- The collection of random variables \(\{X, Z\}\) is independent.
- The collection of random variables \(\{Y, Z\}\) is independent.
- The collection of random variables \(\{X, Y, Z\}\) is independent.
by
Sameer Kailasa