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

We say that Z is exponentially distributed with parameter λ > 0 if the function of Z is given by:
P (Z < z) = 1 − e−λx
(a) Determine and plot the density function of Z.
(b) Calculate E[Z].
(c) Obtain the variance of Z.
(d) Suppose Z1 and Z2 are both distributed as exponential and are independent. Calculate the of their sum:
S = Z1 + Z2
(e) Calculate the mean and the variance of S.

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