Suppose that the lifetime T of a system has a G41 distributi

Suppose that the lifetime T of a system has a G(4,1) distribution. That is, f(t) = (1/6)(t^3)(e^-6) for t>= 0.

Calculate the reliability function of the sysetm in question at time t=4, given that it is still active at time t=2.

Solution

T: G(4,1)

f(t) =  (1/6)(t^3)(e^-6) for t>= 0.

f(4/2) = f(4)/f(2) = 64/6(e^-6)/8/6(e^-6) = 8