Negative Binomial = sum of r iid Geometrics (wait until the r-th success). This is the discrete mirror of Gamma = sum of k iid Exponentials.
✓ 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
A basketball player makes each free throw independently with p = 0.5. Let Y = total number of attempts needed to make exactly r = 3 baskets. (a) Identify the distribution of Y. (b) Compute E[Y], Var(Y). (c) Compute P(Y = 7).
✓ 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.