Geometric & Negative Binomial Distributions (Edexcel A-Level Further Mathematics): Flashcards

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Binomial Distribution
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Key features of binomial distribution model

Two outcomes (win/lose), fixed number of trials

Meaning of nn in X∼B(n,p)X \sim B(n, p)

Number of trials

Meaning of pp in X∼B(n,p)X \sim B(n, p)

Probability of success (win)

Formula for P(X=r)P(X = r) in binomial distribution

(nr)pr(1−p)n−r\binom{n}{r} p^r (1-p)^{n-r}

Cumulative binomial distribution notation

P(X≤a)P(X \leq a)

Calculator mode for exact binomial probability

Binomial PD

Calculator mode for cumulative binomial probability

Binomial CD

Expected value formula for X∼B(n,p)X \sim B(n, p)

E(X)=npE(X) = np

Variance formula for X∼B(n,p)X \sim B(n, p)

Var(X)=npq\text{Var}(X) = npq where q=1−pq = 1 - p

First assumption for binomial model

Trials are independent of previous trials

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Geometric & Negative Binomial Distributions

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Geometric & Negative Binomial Distributions

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Geometric & Negative Binomial Distributions

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Geometric & Negative Binomial Distributions

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