The demand placed on a system is described by a normally distributed random vari

The demand placed on a system is described by a normally distributed random variable with mean 50 and standard deviation of 10. The capacity of the system is modeled by a Weibull random va
Q.1
The demand placed on a system is described by a normally distributed random variable with mean 50
and standard deviation of 10. The capacity of the system is modeled by a Weibull random variable with
mean 65 and standard deviation of 15.
Compute the probability of failure of this system using the Monte Carlo simulation technique.
Q.2
A random variable (X) is modelled as an exponentially distributed with mean 50 units.
Simulate N = 50 samples from this distribution and each sample must contain m = 20 simulated values.
From one simulated sample compute the sample mean i.e. mean of 20 simulated values. Repeat this
process for all N = 50 samples.
The end result will be a sample of 50 values of the sample mean. Using this data answer the following:
(1) Plot its histogram of these mean values.
(2) Use the probability paper method to determine a suitable probability distribution for the sample mean.
(3) Compute the bias and standard error associated with the sample mean estimates.
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