(1)  Show that for a continuous

F(t), h(t)=1/O, t>0 is a constant (i.e. not dependent on t) if and only if T follows an exponential distribution (T~EXP(O)

(2)  Show that if T is LOGNOR(μ,σ), then 1/T is LOGNOR(-μ,σ).

(3) The coefficient of skewness, γ3 is a useful scale-free measure of skewness in the distribution of a random variable.

a. Derive an expression for the coefficient of skewness for the Weibull distribution.

b. Compute γ3 for all combination of B = 0.5, 1, 3, 5 and eta = 50, 100.  Also use the computer to draw a graph of the Weibullpdfs for the same combinations of parameters.

c. Explain the effect that changes in η and β have on the shape of the Weibull density and the effect that they have on γ3.