Binomial distribution
Probability theory · Mathematics
Study notes
Q: Toss a fair coin 5 times. Find P(exactly 3 heads). n = 5, p = 1/2, k = 3. P(X=3) = C(5,3) (1/2)^3 (1/2)^2 = 10 × (1/8) × (1/4) = 10/32 = 5/16. E(X) = 5 × 1/2 = 2.5 heads expected.
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Probability theory · Mathematics
Q: Toss a fair coin 5 times. Find P(exactly 3 heads). n = 5, p = 1/2, k = 3. P(X=3) = C(5,3) (1/2)^3 (1/2)^2 = 10 × (1/8) × (1/4) = 10/32 = 5/16. E(X) = 5 × 1/2 = 2.5 heads expected.