Exercise 2: A Signup Flow's Conversion Probability, Mean & Variance — Possible Solution
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GIVEN
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n = 8, k = 2, p = 0.15

STEP 1: P(EXACTLY 2 CONVERT)
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C(8, 2) = (8 x 7) / (2 x 1) = 28
p^2 = 0.15^2 = 0.0225
(1-p)^(8-2) = 0.85^6 ~= 0.377

P(X=2) = 28 x 0.0225 x 0.377
        ~= 0.2376 (about 23.76%)

STEP 2: E[X]
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E[X] = n x p = 8 x 0.15 = 1.2

The expected number of conversions out of 8 visitors is 1.2.

STEP 3: Var(X)
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Var(X) = n x p x (1-p) = 8 x 0.15 x 0.85 = 1.02

WHY THIS WORKS AS AN ANSWER
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The exact-count probability is computed using this chapter's own full
binomial formula with each term shown, while the mean and variance are
computed using this chapter's own faster np and np(1-p) shortcuts
rather than repeating Chapter 5's full sum-over-every-outcome
calculation, matching the chapter's own worked A/B-test example's
approach exactly.