BrainTok
ENESIT

Stochastic Models: Random variables review for modeling · Discrete Distributions for Counting

How the Bernoulli, binomial, geometric, negative binomial, hypergeometric and Poisson distributions model counts, and how to tell which one fits a real situation.

Stochastic Models · 26 questions

Try 3 questions

1. A machine part fails with probability 0.1 on each independent use. Which distribution models the number of uses until the first failure?

  1. Binomial
  2. Geometric
  3. Poisson
Show the answer

Answer: Geometric

The geometric distribution counts independent trials, each with the same success probability, until the first success (here, the first failure of the part).

2. If each independent use has a 10% chance of failure, how many uses, on average, until the first failure, counting the failing use?

  1. 9 uses
  2. 5 uses
  3. 10 uses
Show the answer

Answer: 10 uses

The mean of a geometric count of trials is 1/p, so with p = 0.1 the average is 10 uses including the one that fails.

3. A batch has 20 items, each independently defective with probability 5%. What is the expected number of defective items?

  1. One defective item
  2. Two defective items
  3. Half a defective item
Show the answer

Answer: One defective item

A binomial count has mean n times p, and 20 × 0.05 = 1.

The rest of the quiz, a few questions at a time

BrainTok asks a few questions from quizzes like these before the apps you choose open, so your screen time turns into learning. For iPhone.

Join the beta

More Industrial Engineering quizzes