Geometric distribution calculator is an online statistical tool to calculate the geometric distribution of a data. In statistics, there are two common versions of the geometric distribution.

If X is defined over the range x=1,2,3,....$\infty$  and has the probability density function,

p(x) = p(1-p)x-1   x=1,2,3,....$\infty$
          = 0                otherwise

where 0 ≤ p ≤ -1, we would say that X has the geometric distribution beginning at 1.

If it is defined over the range x=0,1,2,..... $\infty$ and probability density function is given by,

p(x)=p(1-p)x   x=0,1,2,....$\infty$
       =0                 otherwise

we would say that X has the geometric distribution beginning at 0.


The mean and variance fo r the geometric distribution beginning at 1 are
Mean:$\frac{1}{p}$
Variance:$\frac{1-p}{p^{2}}$
When the distribution begins at 0, the variance is the same but  the mean is $\frac{1-p}{p}$
The given steps helps to find out the geometric distribution:

Step1: Identify the value of p from the question.

Step2: Find out the distribution by substitute the value in the given formula.

p(x)=p(1-p)x   x=0,1,2,3,....$\infty$
     =0    otherwise

Step3: Calculate mean and variance using the given formula.

Mean:$\frac{1-p}{p}$

Variance:$\frac{1-p}{p^{2}}$