📉 SMp(x) Distribution Calculator
Enter a success probability p and a value of x to compute SMp(x), the survival function of the geometric distribution, along with its PMF, CDF, and mean.
What this calculator does
SMp(x) refers to the survival function of a geometric distribution with success probability p, evaluated at x. It gives the probability of observing more than x failures before the first success — in other words, the probability of “surviving” past x trials without success.
How the calculation works
For a geometric distribution counting the number of failures before the first success, the survival function is SMp(x) = P(X > x) = (1 – p)^x, where p is the probability of success on each independent trial. The calculator also reports the probability mass function PMF = p x (1-p)^x, the cumulative distribution function CDF = 1 – (1-p)^(x+1), and the distribution’s mean, (1-p)/p.
This family of formulas is standard for modeling repeated independent trials with a constant success probability, such as the number of attempts needed before a first success. This tool is for general statistics and probability education.