If the failure intensity rate observes the power law function (t) = 𝛼𝛽t 𝛽 −1 , estimate the cumulative number of failures in the intervals of [0, t =10] and [t =10, t =20], respectively, assuming...

If the failure intensity rate observes the power law function (t) = 𝛼𝛽t 𝛽 −1 , estimate the cumulative number of failures in the intervals of [0, t =10] and [t =10, t =20], respectively, assuming the following cases: (1) {𝛼 =30, 𝛽 =0.5}; (2) {𝛼 =10, 𝛽 =1}; and (3){𝛼 =0.5, 𝛽 =2}.