A SMART goal is Specific, Measurable, Attainable, Relevant and Time-Bound.
“I aim to attain my Fellowship in 5 years” fulfils S, A, R and T. Measurable? Number of exams passed so far? Seems inadequate - doesn’t tell me whether I’m on track or not, it’s backward looking. A simple approach: Expected Travel Time = {E[Number of Failures | Passed all exams] + Total number of exams} * E [Time Interval between each exam attempt(T)] Assume: a) T = constant 4 months (3 attempts per year) b) Outcome of each exam attempt is an i.i.d. (independent and identically distributed) Bernoulli random variable c) Total of 15 exams Set X = Number of Failures | Passed all exams ; and p = Probability of passing each exam It follows that, X is a Negative Binomial (15, 1-p) random variable We know E[X] = 15 * (1 – p)/p If p = 40% (usual % who pass an actuarial exam); Expected Travel Time = 12.5 years! Yikes, no!! p = 50%; Expected Travel Time = 10 years…still too long p = 70%; Expected Travel Time = 7.1 years…not bad p = 80%; Expected Travel Time = 6.25 years…good p = 90%; Expected Travel Time = 5.56 years…yes that’s ideal! Is our probability of passing at 70% or higher? (Measure using mock exams?) How do we improve this model?
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