Exponential Distribution Calculator
Calculate probabilities of the exponential distribution step by step
The calculator will find the simple and cumulative probabilities, as well as the mean, variance, and standard deviation of the exponential distribution.
Related calculator: Geometric Distribution Calculator
Your Input
Calculate the various values for the exponential distribution with $$$\lambda = 0.8 = \frac{4}{5}$$$ and $$$x = 2.7$$$.
Answer
Mean: $$$\mu = \frac{1}{\lambda} = \frac{5}{4} = 1.25$$$A.
Variance: $$$\sigma^{2} = \frac{1}{\lambda^{2}} = \frac{25}{16} = 1.5625$$$A.
Standard deviation: $$$\sigma = \sqrt{\frac{1}{\lambda^{2}}} = \frac{5}{4} = 1.25$$$A.
$$$P{\left(X = 2.7 \right)} = 0$$$A
$$$P{\left(X \lt 2.7 \right)}\approx 0.884674878961938$$$A
$$$P{\left(X \leq 2.7 \right)}\approx 0.884674878961938$$$A
$$$P{\left(X \gt 2.7 \right)}\approx 0.115325121038062$$$A
$$$P{\left(X \geq 2.7 \right)}\approx 0.115325121038062$$$A