Mean and variance of the binomial distribution (HSC SSCE Mathematics Extension 1): Flashcards

The average number of expected successes in trials.

How much the actual results differ from the mean.

As $X \sim B(n, p)$ for $n$ trials and success probability $p$.

Mean: $E(X) = np$.

Variance: $Var(X) = np(1-p)$.

Results gather more closely around the mean.

Mean: $E(X) = 10 \times 0.5 = 5$.

Variance: $Var(X) = 2.5$.

Mean: $E(X) = 6$.

Variance: Var(X) = n * p * (1 - p) = 4.2.