(Answered) We say that z is exponentially distributed with parameter a

Finance

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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