# In this simulation the library numpy is used and it is named it $"$np$"$

# We will also use the math library and we will name it math

import numpy as np

import math as math

# The seed below initializes the random generator to always obtain the same random inputs.

# DO NOT CHANGE THIS VALUE AND RERUN THIS CELL EVERYTIME YOU RUN THE PROGRAM.

np$.$random.seed$(3500)$

# Variables are defined in this cell

Cap $=6$ # Capacity of the reservoir

hours $=24$ # $24$ hours in one day

days $=365*100$ # number of days in $100$ years

nHours $=0$ # Counter for number of hours

inflow $=2\mathrm{.}0$ # Inflow of treated water into the reservoir every hour in ML

offDem $=0\mathrm{.}45$ # Offpeak demand

mean$\_$pDem $=2\mathrm{.}6$ # Mean of the demand during peak hours

cov$\_$pDem $=0\mathrm{.}4$ # Coefficient of variation of demand during peak hours

# Because the peak demand log$-$normally distributed the mean and standard deviation of the ln$($pDem$)$ must be obtained

Psi $=$ math.sqrt$($math$.$log$(1+$ cov$\_$pDem$**2))$

Lambda $=$ math.log$($mean$\_$pDem$)-$ Psi$**2/2$

Dem $=$ np$.$empty$($hours$*$days$)$

volume $=$ Cap # initialise the volume equal to the capacity

nFail $=0$ # counter of falures

pFail $=0$ # probability of failure

for day in range$($days$)$:

for hour in range$($hours$)$:

# Define peak demand period

# If peak demand randomly sample values of ln$($pDem$)$ from the lognormal distribution and store them in Dem

# If offpeak demand Dem$[]=0\mathrm{.}45$

if hour$>=7$ and hour:

Dem$[$nHours$]=$ math.exp$($np$.$random.normal$($Lambda$,$Psi$))$

else:

Dem$[$nHours$]=$ offDem

# Perform water balance in reservoir

volume $=$ volume $+$ inflow $-$ Dem$[$nHours$]$

if volume $>=$ Cap:

volume$=$Cap

elif volume :

volume $=0$

if hour$>=7$ and hour:

nFail $=$ nFail $+1$

nHours $=$ nHours $+1$

# calculate and print the probability of damage DURING PEAK HOURS

pFail $=$ nFail$/(($hours$-8)*$days$)$

print$("$The probability of failing to supply the demand is $",$ pFail$).$ Answer the question in the image please.