Repeat part b in the case when the number of dice rolled isn't 18 but is instead a random number that has the Poisson (lambda = 18) distribution.
a) Roll 18 dice and calculate the probability of getting a sum of 108.
b) Roll a random number of dice with a Poisson distribution of lambda = 18 and calculate the expected value of the sum of all dice rolls.
c) Roll 18 dice and calculate the variance of the sum of the dice rolls.
d) Calculate the standard deviation of the sum of the dice rolls.
