# Exponential Distribution#

Time until an event that occurs at rate $$\lambda$$.

Corresponds to a Geometric Distribution for infinite trials of infinitesimal small time slices, such as seconds till the next email arrives.

## Probability Density Function#

$f(x;\lambda) = \lambda e^{-\lambda x} \qquad x \gt 0$

with the rate parameter $$\lambda$$.

import numpy as np
import matplotlib.pyplot as plt
import scipy.stats as st

n = 6
lam1 = 1; lam2 = 0.4
scale1 = 1/lam1; scale2 = 1/lam2
lx = np.arange(0,n,0.1)

plt.plot(lx, st.expon.pdf(lx, 0, scale1), label="λ = {}".format(lam1) )
plt.plot(lx, st.expon.pdf(lx, 0, scale2), label="λ = {}".format(lam2) )
plt.show()