Consider the random variable, X, with cumulative distribution function FX(x)= (1+x)",0 2X >> 1) To do this, you will first need to calculate PriX > 1) and Prix > 2). In reliability engineering and actuarial science, the survival function (of a device, person, system etc.) is defined as S(t) = P {T> t}, where T is the random variable representing the lifetime of the device, and t > 0 is time. Here, {T> t} is the event that the lifetime of the device has not yet expired at time t and the device is still in operation. The hazard rate, denoted h(t), is defined as the rate at which the device fails at time t, on the condition that it has survived until at least time t. h(t) = lim 0++ = lim 7-0 P{t 1 in part (c).