Programming: Homework at page 122

homework.jl

#= 
This is a program to simulate Homework @probability.pdf page 122
Author: Evan MU
=#

# source type A
rate_A = 10
num_A = 20
prob_A = 0.1
# 1-prob_A is idle probability of source type A

# source type B
rate_B = 1
num_B = 80
prob_B = 0.05
# 1-prob_B is idle probability of source type B

# calculate Expectation of each source
Exp_A = rate_A * prob_A
Exp_B = rate_B * prob_B

# calculate Variance of each source
Var_A = (rate_A^2)*prob_A*(1-prob_A)
Var_B = (rate_B^2)*prob_B*(1-prob_B)

Exp_total = num_A*Exp_A + num_B*Exp_B
Var_total = num_A*Var_A + num_B*Var_B
R_total = num_A*rate_A+num_B*rate_B

Copt = min(R_total, Exp_total+3*sqrt(Var_total))

output = "The answer is $(Copt)"

println(output)