Question

What is the Mean, Var(X) and sd of the Binomial Distribution?

Answer 1

The mean, variance, and standard deviation of the binomial distribution can be calculated using specific formulas: µ = np, o² = npq, o = √(npq).

Step-by-step explanation:

The mean, variance, and standard deviation of a binomial distribution can be calculated using specific formulas:

• The mean (µ) is equal to the number of trials (n) multiplied by the probability of success (p): µ = np
• The variance (o²) is equal to the number of trials (n) multiplied by the probability of success (p) multiplied by the probability of failure (q): o² = npq
• The standard deviation (o) is equal to the square root of the variance: o = √(npq)

For example, if you have 50 trials with a success probability of 0.4, the mean would be 50 * 0.4 = 20, the variance would be 50 * 0.4 * 0.6 = 12, and the standard deviation would be √(12) ≈ 3.46.