1. Answer the following: a) What type of continuous random variable can be model

Question

1. Answer the following:

        a) What type of continuous random variable can be modeled by

                 - an Erlang distribution?

                 - a Gamma distribution?

                 - a Weibull distribution?

                 - a Beta distribution?

        b) Compute the gamma function (r) if r = 0, 1, 3 and 4

        c) What distribution would we use to compute time until failure of a machine?

        d) If a random variable Y = e(W), where W is a random variable that has a normal

distribution. What do we call the distribution of Y? Give an example of a random variable

that might possess such a distribution.

Explanation / Answer

Where the same random variable also follow another distribution of same kind r = r     0 = 0 = 1; 1 = 1= 1 ; 3 = 3= 6     4 = 4=24 Exponential distribution We call the distribution of Y as log normal distribution . as the positive random variable is said to have a log normal distribution, if log xis normally distributed

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