已知 density f(x) = 1/theta. 对 f 积分得到 cdf F(x) = integral of f from 0 to x = x/theta. Thus survival function S(x) = 1 - F(x) = 1 - x/theta.
Now we compute hazard function by its definition: h(x) = f(x) / S(x) = 1 / (theta - x).
Finally, mean residual life given that the organism has survived at time t is: E(X-x | X>=x) = E(X|X>=x) - x = (integral of x*f(x) from x to theta) / S(x) - x = (theta - x)/2.
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