10. a.If f(t) = tm and g(t) = tn, where m and n are positive integers, show that f∗g=tm+n+1∫10um(1−u)ndu.f∗g=tm+n+1∫01um(1−u)ndu. b.Use the convolution theorem to show that ∫10um(1−u)ndu=m!n!(m+n+1)!.∫01um(1−u)ndu=m!n!(m+n+1)!. c.Extend the result of part b to the case where m and n are positive numbers but not necessarily integers.

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A: If Z~ N(0,1)   which means clearly it is standardized normal distribution table.

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A: The required proofs are detailed below.

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A: