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If X(t) is a Wiener process with EX(t) = vt and var X(t) = σ2t (where v > 0) and if M(t) = max0≦τ≦tX(τ) and Ta is the time of first passage through level a (where a > 0) we show that
where 
is the coefficient of variation of Ta. Applications of the result to the “maturity-time” representation of cell-growth and to queues with heavy traffic are discussed.
