Geometric Distribution Calculator
The calculator will find the simple and cumulative probabilities, as well as the mean, variance, and standard deviation of the geometric distribution.
Related calculator: Exponential Distribution Calculator
Your Input
Calculate the various values for the geometric distribution with $$$n = 7$$$ and $$$p = 0.5 = \frac{1}{2}$$$ (include a success trial).
Answer
Mean: $$$\mu = \frac{1}{p} = \frac{1}{\frac{1}{2}} = 2$$$A.
Variance: $$$\sigma^{2} = \frac{1 - p}{p^{2}} = \frac{1 - \frac{1}{2}}{\left(\frac{1}{2}\right)^{2}} = 2$$$A.
Standard deviation: $$$\sigma = \sqrt{\frac{1 - p}{p^{2}}} = \sqrt{\frac{1 - \frac{1}{2}}{\left(\frac{1}{2}\right)^{2}}} = \sqrt{2}\approx 1.414213562373095$$$A.
$$$P{\left(X = 7 \right)} = 0.0078125$$$A
$$$P{\left(X \lt 7 \right)} = 0.984375$$$A
$$$P{\left(X \leq 7 \right)} = 0.9921875$$$A
$$$P{\left(X \gt 7 \right)} = 0.0078125$$$A
$$$P{\left(X \geq 7 \right)} = 0.015625$$$A