We are given $$h(t)=\lambda exp(\theta t)$$, h(t) is the harzard function defined in fields of biostatistics. It has relationship with f(t) in the following way:
I have reached the step of finding $$f(t)=\lambda \exp(t/2-2\lambda \exp(t/2)+2\lambda)$$
But I am unable to derive the expectation by using $$E(x)=\int tf(t)dt$$
Could someone please show me how to find the expectation of the Gompertz distribution?