The distribution of residence times in a standard size continuous stirred tank reactor (CSTR) is known to be exponential with β = 1, i.e., E (1). If X is the residence time for a reactor that is ?ve times the standard size, then its distribution is also known as E (0.2). On the other hand, Y , the residence time in an ensemble of ?ve identical, standard size CSTR's in series, is known to be gamma distributed with α = 5; β = 1.

(i) Plot the pdf f (x) for the single large CSTR's residence time distribution and the pdf f (y) for the ensemble of ?ve identical small reactors in series. Determine the mean residence time in each case.

(ii) Compute P (Y ≤ 5) and compare with P (X ≤ 5)