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The exponential distribution has pdf p(y)=e-yfor ygt;0. Its mean is 1/and its standard deviation is also 1/.
The exponential distribution has pdf p(y)=e-yfor y>0. Its mean is 1/and its standard deviation is also 1/. If you have reason to believe an exponential model would be appropriate for your process, should you use the usual estimator of the standard deviation (the one that uses n-1 in the denominator), or should you use the sample average Y to estimate the standard deviation? Perform a simulation study for a sample of n=20 observations from an exponential distribution with mean 4. To accomplish this, perform the following steps, similar to the analysis shown in Table 11.3 for the Poisson distribution.
A. Generate a set of n=20 observations from an exponential distribution with mean 4.0, and hence with standard deviation that is also 4.0. Use either built-in random number generators from your software or use the inverse cdf method. Calculate both the usual estimator of the standard deviation and the estimator Yusing your sample of n=20 observations. Compare these estimates to the true standard deviation: for this sample, which is the better estimate of standard deviation, the usual estimate or Y ?