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Find $$$P{\left(X = 18 \right)}$$$ for geometric distribution with $$$n = 18$$$ and $$$p = \frac{1}{8}$$$

The calculator will find the probability that $$$X = 18$$$ for the geometric distribution with $$$n = 18$$$ and $$$p = \frac{1}{8}$$$.

Related calculator: Exponential Distribution Calculator

There are two types of geometric distributions: either $$$X$$$ is the number of trials up to and including the first success, or $$$X$$$ is the number of trials (failures) until the first success.

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Your Input

Calculate the various values for the geometric distribution with $$$n = 18$$$ and $$$p = \frac{1}{8}$$$ (include a success trial).

Answer

Mean: $$$\mu = \frac{1}{p} = \frac{1}{\frac{1}{8}} = 8$$$A.

Variance: $$$\sigma^{2} = \frac{1 - p}{p^{2}} = \frac{1 - \frac{1}{8}}{\left(\frac{1}{8}\right)^{2}} = 56$$$A.

Standard deviation: $$$\sigma = \sqrt{\frac{1 - p}{p^{2}}} = \sqrt{\frac{1 - \frac{1}{8}}{\left(\frac{1}{8}\right)^{2}}} = 2 \sqrt{14}\approx 7.483314773547883.$$$A

$$$P{\left(X = 18 \right)}\approx 0.012913587642949$$$A

$$$P{\left(X \lt 18 \right)}\approx 0.896691298856407$$$A

$$$P{\left(X \leq 18 \right)}\approx 0.909604886499356$$$A

$$$P{\left(X \gt 18 \right)}\approx 0.090395113500644$$$A

$$$P{\left(X \geq 18 \right)}\approx 0.103308701143593$$$A