Please see the question

(30 pts) You suspect that the time to failure of a certain electronic item is exponentially distributed with parameter A, i.e., with density function f(x) = Aexp()m:), 3: > O and cdf F(ac) = 1 exp()\\x), :1: > 0. You have data on the failure times of 100 items over a 30day time interval. Denote these data points by Y1, ...,Y100. For each item that failed during this period of time (starting brand new at time 0) you observe the time to failure, but for items that did not fail you observe 30 (i.e., the length of the observation period). That is, if Y, = 30 for some item, you do not know the time to failure for that item, but you know that it is greater than or equal to 30 days. (a) (10 pts) Write down the cumulative distribution function (cdf) of Y, i.e., the observed (censored) time to failure of the items. (b) (20 pts) Compute the maximum likelihood estimator of A given the observations Y1, --,Yioo