import scipy.stats as st
import numpy as np

Exponential = st.expon

X = Exponential(scale = 5000)

X.cdf(2500) # cumulative distribition function

0.3934693402873666

1 - X.cdf(6000)

0.3011942119122022

# 2 b
X.ppf(.1)

526.8025782891316

-5000 * np.log(1 - 0.1)

526.8025782891314

# 3 a
X = Exponential(scale = 20)
X.cdf(10)

0.3934693402873666

X.ppf(0.5)

13.862943611198906

X.ppf(1)

inf

X.pdf(2)

0.04524187090179797