Binomial Probability Mass Function

A Binomial variable counts the number of successes in n independent Bernoulli(p) trials. Its PMF gives the probability of exactly k successes; its CDF gives the probability of at most k.

P(X = k) = \binom{n}{k} p^k (1-p)^{n-k}

Task: write binomial_pmf_cdf(n, p, k) returning [pmf, cdf], each rounded to 4 decimal places, where cdf = P(X \le k).

cdf is the running sum of the pmf from 0 up to and including k.
With n = 1, this collapses back to a plain Bernoulli trial.

Binomial Probability Mass Function

Examples

Hints