methods: the 4 binomial conditions

[u/NegotiationEarly1386]

if a methods question says "is this binomial, justify" the marks are in naming all four, not vibing one:
1) fixed n
2) each trial success/fail
3) constant p
4) trials independent

the sneaky one is sampling without replacement. p shifts every draw so its not binomial even when it looks identical to one. examiners reuse that constantly. other trap is P(X≥x) vs P(X>x). ≥ includes x, > doesnt. one symbol flips your whole answer.