Why this chapter matters
Discrete models describe counts and repeated yes-no processes that appear in reliability, quality, and survey settings.
What you will learn
- Construct and interpret probability mass functions.
- Calculate expected value and standard deviation for a discrete variable.
- Use binomial and geometric models under their assumptions.
Lessons in this chapter
- Random variables and distribution tablesTranslate outcome rules into a valid probability distribution. Read the full guide →
- Expected value and variabilityCompute mean and variance from a discrete distribution.
- Binomial modelIdentify fixed-trial Bernoulli settings and compute binomial probabilities.
- Geometric modelModel the number of trials until first success and interpret long-run behavior.
Study task
For a customer support process with 0.8 first-contact resolution chance, define a geometric variable for trials to success and compute two example probabilities.
Chapter checkpoint
What conditions justify a binomial model?
A fixed number of trials, independent trials, only success or failure outcomes, and a constant success probability across trials.