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

Exponential examples from https://roualdes.us/lecturenotes/exponential

# 1.
X = st.expon(scale = 5000) # scale = 5000 sets lambda as we want

# a.
X.cdf(2500)

0.3934693402873666

# b.
1 - X.cdf(6000)

0.3011942119122022

Inverse CDF

def invCDF(p, lamda = 1):
    return -lamda * np.log(1 - p)

X = st.expon(scale = 5)

X.ppf(0.3)

1.7833747196936622

invCDF(0.3, lamda = 5)

1.7833747196936622