User:Skbkekas, CC BY 3.0 · CC-BY-3.0 · Wikimedia Commons
Geometric is 'wait time until the first Bernoulli success'. The Negative Binomial generalises this to 'wait until the k-th success'.
✓ Intro · expand
Try first (productive failure)
Before the worked example: spend 60 seconds taking your best shot at this.
A guess is fine — being briefly wrong about a problem makes the explanation
land harder when you read it. This appears once per tutorial; skip
if you already know the trick.
60s
✓ Try first · expand
Worked example
An insurance agent makes cold calls; each call is independently successful with probability p = 0.2. Let X = number of calls until (and including) the first success. (a) Identify the distribution. (b) Compute E[X], Var(X). (c) Compute P(X = 5) and P(X > 5).
✓ Worked example · expand
Practice 1 of 3Type a fraction, decimal, or expression — mathjs parses it.
✓ Practice · expand
Reflection
Where does this distribution sit in the story chain — what question does it answer that the previous distribution couldn't? Try to recall the key moment formulas (mean, variance) without looking them up.
