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5. Consider the random variable X with the following distribution function for a > 0, β...

5. Consider the random variable X with the following distribution function for a > 0, β > 0:
FX (z) = 0 for z ≤ 0
​= 1 – exp [–(z/a)β] for z > 0 (where exp y = ey)
(a) Determine the inverse function of FX (z), where 0 < z < 1.
(b) Let a = β = 2 for the random variable X, and define the numbers u1 = .33 and u2 = .9. Use the inverse transform method discussed in class to produce values Y1 and Y2 for a random variable Y that has the same distribution as X.
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