Skip to content

AI & ML · Probability for ML

Maximum likelihood

201 problems in this skill, each with a solver-verified answer key. Answers are checked the moment you submit — with a hint if you want one and a worked solution afterwards.

What the problems look like

A few statements from this skill. Answers, hints and worked solutions live in the practice session.

  1. Warm-up

    In n=20n = 20 independent Bernoulli trials, the number of successes is k=19k = 19. The log-likelihood is ℓ(p)=kln⁡p+(n−k)ln⁡(1−p)\ell(p) = k\ln p + (n-k)\ln(1-p). Find the maximum likelihood estimate p^\hat p of the success probability, giving your answer as a fraction.

  2. Warm-up

    In n=7n = 7 independent Bernoulli trials, the number of successes is k=1k = 1. The log-likelihood is ℓ(p)=kln⁡p+(n−k)ln⁡(1−p)\ell(p) = k\ln p + (n-k)\ln(1-p). Find the maximum likelihood estimate p^\hat p of the success probability, giving your answer as a fraction.

  3. Warm-up

    In n=20n = 20 independent Bernoulli trials, the number of successes is k=9k = 9. The log-likelihood is ℓ(p)=kln⁡p+(n−k)ln⁡(1−p)\ell(p) = k\ln p + (n-k)\ln(1-p). Find the maximum likelihood estimate p^\hat p of the success probability, giving your answer as a fraction.

Problems shown under their original terms: Generated (template, solver-computed).

Practice this free, right now

Unlimited math practice is on the free plan — no card, no trial clock.

Practice freeLog in and practise this skill

See every Probability for ML skill for ai & ml