find attcahment - 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...

find attcahment - 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 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.