Question: Each day, John is jogging the same route. The times it takes are i.i.d. r.v.s assuming values between 30 and 31 minutes. Find the distribution

Each day, John is jogging the same route. The times it takes are i.i.d. r.v.’s assuming values between 30 and 31 minutes. Find the distribution of the best result in a week and its expected value in the case where for each separate day

(a) The distribution is uniform on [30,31];

(b) The distribution has the density f(x) = 2(x−30) for x ∈ [30,31]. Compare the expectations and interpret the difference.

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