There is a question about STAT that I want someone can helps

There is a question about STAT that I want someone can helps me solve it.\\

7. Re-consider the failure time of the lightbulbs example in previous homework. Define X=time to failure, and assume this random variable is exponentially distributed with density function f(x; lambda) = lambda e^-lambda x Now assume lambda = 3. (a) First simulate a random sample of size 100 from this distribution. What is your sample mean? (b) Imagine we didn\'t know the true distribution with lambda = 3, but we kind of know the underlying distribution is exponential distribution (from your probability course). Based on your simulated sample, what is your best guess of the true lambda in the exponential distribution? (c) Because this estimator coincides with the Maximum Likehood Estimator (MLE), by the property of MLE, this estimator is asymptically normal distribution. That is, as sample size grows to infinity, the limiting distribution of this esimator is normal distribution. Provide an interval estimate for the true lambda paremater.

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