Description

CENG 222
Statistical Methods for Computer Engineering
Assignment #3
In a small village, several vehicles use a bridge to cross over a river. Everyday several motorcycles, automobiles, and trucks use this bridge.
The number of motorcycles that pass over the bridge on a day is a Poisson random variable with λ = 40.
The number of automobiles that pass over the bridge on a day is a Poisson random variable with λ = 30.
The number of trucks that pass over the bridge on a day is a Poisson random variable with λ = 20.
The weight of each motorcycle is a Gamma distributed random variable in kilograms with α = 16 and λ = 0.15.
The weight of each automobile is a Gamma distributed random variable in kilograms with α = 60 and λ = 0.05.
The weight of each truck is a Gamma distributed random variable in kilograms with α = 84 and λ = 0.01.
(a) Conduct a Monte Carlo study to estimate the probability that the total weight of all thevehicles that pass over the bridge in a day is more than 220 tons. With probability 0.99, your answer should differ from the true value by no more than 0.02. Use Normal approximation to determine the size of your Monte Carlo simulation. Use Example 5.9 from the book to sample from the Poisson distribution and Example 5.11 to sample from the Gamma distrubution.
(b) Based on the study in part (a), estimate the total weight, X, of all the vehicles that pass over the bridge in a day.
(c) Estimate Std(X) and comment on the accuracy of your estimator of X.
Submission
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