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Flip to reveal answersWhat is the mean of X ~ B(n, p)?
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All 9 Flashcards — Binomial mean and variance
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Question
What is the mean of X ~ B(n, p)?
Answer
E(X) = np.
Question
What is the variance of X ~ B(n, p)?
Answer
Var(X) = np(1 − p).
Question
What is the standard deviation of a binomial?
Answer
√(np(1 − p)).
Question
What does the binomial mean represent?
Answer
The expected number of successes in n trials.
Question
Common slip in the variance?
Answer
Using np or np² instead of np(1 − p) — you must multiply by both p and (1 − p).
Question
How do you find p from the mean and variance?
Answer
variance ÷ mean = 1 − p, so p = 1 − variance/mean.
Question
How do you then find n?
Answer
n = mean ÷ p.
Question
Are np and np(1 − p) in the formula booklet?
Answer
Yes — both the binomial mean and variance are given.
Question
X ~ B(50, 0.2): mean and variance?
Answer
Mean 10, variance 8.
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Topic 4.8 hub
Binomial distribution
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