Exercise · ZW-BERNOULLI-DISTRIBUTION-008 · ★★☆ Intermediate
For which value of \(p\) is the variance of a Bernoulli variable largest?
Choose one option.
Show answer
- D. \(p=\tfrac12\)
Explanation
\(p(1-p)\) equals \(\tfrac14\) at \(p=\tfrac12\) and less elsewhere; with \(p=1\) there is no uncertainty and the variance is 0.
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-009 A Bernoulli variable has Var(X)=0.16 and p<tfrac12. What is p?
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