Okay, so given that it is an exponential distribution, I can prove that the hazard is constant, since I know the cdf and pdf of an exponential:
However, can someone help with how to prove in the other direction. i.e. how to show that given that the reliability of a random variable with cdf F is defined to be and that the hazard is that this implies the hazard of the variable is constant only if the variable is exponential?
EDIT: Nevermind, I solved it.