A random variable (X) is modelled as an exponentially distributed with mean 30 units. Simulate N = 50 samples from this distribution, and every sample must have 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) Place its histogram of these mean values.
(2) Use the probability paper method to verify a suitable probability distribution for the sample mean.
(3) Compute the bias and standard error associated with the sample mean estimates.