Please answer the following question, it is about survival analysis. Thank you.

1. (30 points) Suppose that a failure time T follows an exponential distribution. (a) If the mean value of T is 5, determine its density function, hazard function, cumulative hazard function and survival function. (b) If the mean value of T is 5, what is the median survival time for this distribution. (c) In a clinical study, we observe the following failure times T, with "+" indicating cen- sored subjects: 22, 2, 48, 85, 160, 238, 56+, 94+, 51+, 12, 171, 80, 180, 4, 90, 180+, 3. We assume that T' follows an exponential distribution and is subject to independent censoring C, what is the MLE for A as the parameter for the exponential distribution