Question

Problems 95 Consider a binomial experiment with 2 trials and p = 0.4. a. Compute the probability of 1 success, f(1). b. Compute f(0). Compute f(2). Find the probability of at least one success. e. Find the expected value, variance, and standard deviation.

Answer 1

n = 2

p = 0.4

f(x) = 2Cx * 0.4^x * (1 - 0.4)^2-x

a) f(1) = 2C1 * 0.4¹ * 0.6¹ = 0.48

b) f(0) = 2C0 * 0.4⁰ * 0.6² = 0.36

c) f(2) = 2C2 * 0.4² * 0.6⁰ = 0.16

d) P(X > 1) = 1 - f(0) = 1 - 0.36 = 0.64

e) Expected value = n * p = 2 * 0.4 = 0.8

Variance = n * p * (1 - p) = 2 * 0.4 * 0.6 = 0.48

Standard deviation = sqrt(n * p * (1 - p)) = sqrt(2 * 0.4 * 0.6) = 0.69

Answer 2

Standard deviation

(to 4 decimals