Question: We say that Z is exponentially distributed with parameter A > 0 in the distribution function of Z is given by: P(Z < z) =

We say that Z is exponentially distributed with parameter A > 0 in the distribution function of Z is given by:

P(Z < z) = 1 – e–kz

(a) Determine and plot the density function of Z.

(b) Calculate the E[Z].

(c) Obtain the variance of Z.

(d) Suppose Z1 and Z2 are both distributed as exponential and an independent. Calculate the distribution of their sum:

S =Z1 + Z2

(e) Calculate the mean and the variance of S.


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