where Q is measured in tons/day, XI represents units of labor per day, X2 represents units of capital per day, and V = eB, with e - N(O, a2 ).

a. Derive the probability density function of the random variable V. (What you will have derived is a PDF that is a member of the "log-normal" family of densities. In general, if X - N(/-L, a2 ), Y =

eX - log-normal, with mean = exp(/-L + a 2/2), variance = exp(2/-L + 2a2 ) - exp(2/-L + a2 ), and /-L~ =

exp[r/-L + 1/2r2a 2 ]).