Exercise · ZW-BERNOULLI-DISTRIBUTION-009 · ★★★ Advanced
A Bernoulli variable has \(\operatorname{Var}(X)=0.16\) and \(p<\tfrac12\). What is \(p\)?
Choose one option.
Show answer
- C. \(0.2\)
Explanation
Solve \(p(1-p)=0.16\), i.e. \(p^2-p+0.16=0\), with roots \(0.2\) and \(0.8\); with \(p<\tfrac12\) we get \(0.2\).
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?
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