Exercise · ZW-BERNOULLI-DISTRIBUTION-010 · ★★★ Advanced
If \(X\) is Bernoulli, which statement is true?
Choose one option.
Show answer
- A. \(X^2=X\)
Explanation
Since \(X\) is only 0 or 1, \(X^2=X\). The others fail: \(p=p(1-p)\) only if \(p=0\), the variance is \(p(1-p)\) and \(X\) is never 2.
Review the concept: Bernoulli distribution
A Bernoulli variable \(X\) only takes the values 1 (success) and 0 (failure); its only parameter \(p\) is the probability \(P\) of success.
\[P(X=1)=p,\quad P(X=0)=1-p\]
More practice problems: bernoulli distribution
- ZW-BERNOULLI-DISTRIBUTION-001 A Bernoulli variable has p=0.3. Compute E[X].
- ZW-BERNOULLI-DISTRIBUTION-002 A Bernoulli variable has p=0.3. Compute Var(X).
- ZW-BERNOULLI-DISTRIBUTION-003 Which of these variables is Bernoulli?
- ZW-BERNOULLI-DISTRIBUTION-004 A fair die is rolled and X=1 if a 6 shows, X=0 otherwise. Compute Var(X).
- ZW-BERNOULLI-DISTRIBUTION-005 A fair die is rolled and X=1 if a multiple of 3 shows, X=0 otherwise. Compute E[X].
- ZW-BERNOULLI-DISTRIBUTION-006 If X is Bernoulli with p=0.4, compute E[X^2].
- ZW-BERNOULLI-DISTRIBUTION-007 If X is Bernoulli and E[X]=0.6, compute Var(X).
- ZW-BERNOULLI-DISTRIBUTION-008 For which value of p is the variance of a Bernoulli variable largest?