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Mathematics · University

Variance of a binomial count

Assume a fixed number of independent trials with the same success probability.

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Method and conditions

Assume a fixed number of independent trials with the same success probability.

Var(X) = np(1−p)

Worked examples

Let X be binomial with n = 160 and success probability p = 0.4. Find Var(X). Round the final result to 4 decimal places if needed.

Independent Bernoulli variances add: 160 × 0.4 × (1 − 0.4).

38.4

Let X be binomial with n = 167 and success probability p = 0.1. Find Var(X). Round the final result to 4 decimal places if needed.

Independent Bernoulli variances add: 167 × 0.1 × (1 − 0.1).

15.03

Try it

  1. Let X be binomial with n = 56 and success probability p = 0.1. Find Var(X). Round the final result to 4 decimal places if needed.

  2. Let X be binomial with n = 30 and success probability p = 0.3. Find Var(X). Round the final result to 4 decimal places if needed.

Check your work

Answers and marking notes
  1. 5.04

    Independent Bernoulli variances add: 56 × 0.1 × (1 − 0.1).

  2. 6.3

    Independent Bernoulli variances add: 30 × 0.3 × (1 − 0.3).

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