Ignoring the fact that the bar exam is only given twice a year, let us suppose...
Ignoring the fact that the bar exam is only given twice a year, let us suppose that new lawyers arrive in Los Angeles according to a Poisson process with mean 300 per year. Suppose that each lawyer independently practices for an amount of time T with a distribution function F(t) = P(T <= t) that has F(0) = 0 and mean 25 years. Show that in the long run the number of lawyers in Los Angeles is Poisson with mean 7500.
Homework Answers
each year 300 new lawyers arrive on average
a lawyer practises for 25 years on average
going by the average if we start with 0 lawyers it will be 25 years before a lawyer stops their practise
and in 25 years :
no. of lawyers arrive = 25*300 = 7500
therefore we can say that in the long run number of lawyers in Los Angeles is Poisson with mean 7500.
P.S. (please upvote if you find the answer satisfactory)
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