In a small village, several vehicles use a bridge to cross over a river. Everyday several...

Transcribed Image Text:

In a small village, several vehicles use a bridge to cross over a river. Everyday several automobiles and trucks use this bridge. The number of automobiles that pass over the bridge on a day is a Poisson random variable with A = 50 and the number of trucks that pass over the bridge on a day is a Poisson random variable with A = 10. The weight of each automobile is a Gamma distributed random variable in kilograms with a = 190 and X = 0.15. The weight of each truck is a Gamma distributed random variable in kilograms with a = 110 and A = 0.01. The bridge is not safe if the total weight of all the vehicles that pass over the bridge on a day is more than 200 tons. You are asked to estimate the probability of this by conducting a Monte Carlo simulation study. Q1. (15 pts.) (a) Use Normal approximation to determine the size of your Monte Carlo simulation so that with probability 0.99, your answer should differ from the true value by no more than 0.02. (5pts) Implement a Matlab/Octave code that does this simulation. As the size of the simulation use your answer in part a of Q1. In your report provide the following; Estimate the probability that the total weight of all the vehicles that pass over the bridge on a day is more than 200 tons. Estimate the total weight, X, of all the vehicles that pass over the bridge on a day. Estimate Std(X) and comment on the accuracy of your estimator of X. In a small village, several vehicles use a bridge to cross over a river. Everyday several automobiles and trucks use this bridge. The number of automobiles that pass over the bridge on a day is a Poisson random variable with A = 50 and the number of trucks that pass over the bridge on a day is a Poisson random variable with A = 10. The weight of each automobile is a Gamma distributed random variable in kilograms with a = 190 and X = 0.15. The weight of each truck is a Gamma distributed random variable in kilograms with a = 110 and A = 0.01. The bridge is not safe if the total weight of all the vehicles that pass over the bridge on a day is more than 200 tons. You are asked to estimate the probability of this by conducting a Monte Carlo simulation study. Q1. (15 pts.) (a) Use Normal approximation to determine the size of your Monte Carlo simulation so that with probability 0.99, your answer should differ from the true value by no more than 0.02. (5pts) Implement a Matlab/Octave code that does this simulation. As the size of the simulation use your answer in part a of Q1. In your report provide the following; Estimate the probability that the total weight of all the vehicles that pass over the bridge on a day is more than 200 tons. Estimate the total weight, X, of all the vehicles that pass over the bridge on a day. Estimate Std(X) and comment on the accuracy of your estimator of X.