Statistics • Discrete Random Variables and Their Probability Distributions
For a binomial random variable with parameters n and p, the mean and standard deviation are:
μ = n · p
σ = √(n · p · q)
where q = 1 − p.
n and p, then press Calculate.
For X ~ Binomial(n, p), the mean is mu = n x p. It represents the expected number of successes in n trials.
First compute the variance sigma^2 = n x p x (1 - p), then take the square root: sigma = sqrt(n x p x (1 - p)).
q is the probability of failure on each trial and equals 1 - p. The variability depends on both success and failure probabilities.
Use them when you have a fixed number of trials, each trial has two outcomes, trials are independent, and the success probability p stays constant.