Question no. 5 We consider the process {X(t), t > 0} defined by X(t) = (tan Y)t, for t 20, where Y is a random variable

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Question No 5 We Consider The Process X T T 0 Defined By X T Tan Y T For T 20 Where Y Is A Random Variable 1 (51.88 KiB) Viewed 75 times

Question no. 5 We consider the process {X(t), t > 0} defined by X(t) = (tan Y)t, for t 20, where Y is a random variable having a uniform distribution on the interval (-7/2,1/2). Calculate the probability P[3 t € (0,1): X(t) ¢ [0,1]]. In other words, calculate the probability that the process {X(t), t > 0) leaves the interval (0, 1) between 0 and 1. Indication. It can be shown that the r.y. W := tan Y has the following density function: 1 fw(w) for WER #(w2 +1) That is, W has a Cauchy distribution, or a Studentio distribution with one degree of freedom.