A survival time T is exponentially distributed if its survival function takes the form a) Find the density function and the hazard rate α(t) for the exponential distribution. A survival time T...

A survival time T is exponentially distributed if its survival function takes the form

a) Find the density function

and the hazard rate α(t) for the exponential distribution.

A survival time T follows a Weibull distribution if its hazard rate takes the form

b) Find the survival function S(t) and the density function f(t) for a Weibull distribution.

A survival time T is gamma distributed if its density function takes the form

c) Find expressions for the survival function S(t) and the hazard rate α(t) of the gamma distribution using the (upper) incomplete gamma function