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Flip to reveal answersWhen is X binomial, X ~ B(n, p)?
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All 9 Flashcards — Binomial probabilities
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Question
When is X binomial, X ~ B(n, p)?
Answer
Fixed number n of independent trials, two outcomes each, with constant success probability p.
Question
What does binompdf(n, p, k) give?
Answer
P(X = k) — the probability of exactly k successes.
Question
What does binomcdf(n, p, k) give?
Answer
P(X ≤ k) — the probability of at most k successes.
Question
State the binomial probability formula.
Answer
P(X = k) = ⁿCₖ pᵏ (1−p)ⁿ⁻ᵏ.
Question
How do you find P(X ≥ k)?
Answer
1 − P(X ≤ k − 1) = 1 − binomcdf(n, p, k − 1).
Question
How do you find P(a ≤ X ≤ b)?
Answer
binomcdf(n, p, b) − binomcdf(n, p, a − 1).
Question
How do you find P(at least one)?
Answer
1 − P(X = 0).
Question
Why might a 'without replacement' situation not be binomial?
Answer
The probability of success changes between trials, so p is not constant.
Question
Finding n for 'at least one' — round up or down?
Answer
Round up, since you need to reach the target probability with a whole number of trials.
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Topic 4.8 hub
Binomial distribution
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