Binomial Distribution (Edexcel A-Level Further Mathematics): Quizzes

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Binomial Distribution
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What are the two key features of a binomial distribution?

Two outcomes and fixed trials

In the notation X∼B(25,0.7)X \sim B(25, 0.7), what does 2525 represent?

Number of trials

What is the 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}

What does P(X≤3)P(X \leq 3) represent for a binomial distribution?

Sum of P(X=0)P(X=0) to P(X=3)P(X=3)

Which calculator mode finds P(X=12)P(X = 12) for a binomial distribution?

Binomial PD

How do you calculate P(X>4)P(X > 4) for X∼B(15,0.3)X \sim B(15, 0.3)?

1−P(X≤4)1 - P(X \leq 4)

For X∼B(n,p)X \sim B(n, p), what is the expected value E(X)E(X)?

npnp

For X∼B(n,p)X \sim B(n, p), what is Var(X)\text{Var}(X) where q=1−pq = 1-p?

npqnpq

Which assumption is needed for a binomial model?

Outcomes are independent

How do you find P(8≤X<11)P(8 \leq X < 11) for X∼B(12,0.1)X \sim B(12, 0.1)?

P(X≤10)−P(X≤7)P(X \leq 10) - P(X \leq 7)

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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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