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Statistics for finance · level 2

Binomial mean and spread

Counting successes out of n tries: the mean is np and the spread is the root of npq. For rare events the Poisson shortcut applies — mean and variance are both np.

Theory: Derivatives & Pricing

Worked example: n = 500, p = 10%. Standard deviation of the count?

mean50
variance45
σ6.71

Step by step

  1. 1

    Mean

    n p = 500 × 10% = 50

  2. 2

    Variance

    n p (1 − p) = 45

  3. 3

    Standard deviation

    √45 = 6.71

n = 500, p = 10%. Standard deviation of the count? = 6.71

The theory behind it

Intuition

For n independent trials, expect n·p successes with variance n·p·q — the fast way to sanity-check a conversion forecast.

Common pitfalls

  • ×Using the binomial when trials are dependent.
  • ×Reporting variance where standard deviation is wanted.

In the interview

Funnel and campaign-response rounds.