Assignment:
Computer simulations and laboratory measurements have indicated that the time between cycle slips is exponentially distributed; that is, the distribution function of the time between cycle slips, T, is given by
p(T) = 1 -exp (-T / Tm)
Given this distribution function, find the mean time between cycle slips and the variance about this mean as functions of Tm. If the mean time between cycle slips is 1 day, what is the probability of cycle slips less than 1 hour apart? More than 3 days apart?
Provide complete and step by step solution for the question and show calculations and use formulas.