Question: Question We are given a stick that extends from 0 to . Its length, , is the realization of an exponential random variable , with

Question

We are given a stick that extends from 0 to . Its length, , is the realization of an exponential random variable , with mean1 . We break that stick at a pointthat is uniformly distributed over the interval[0,] .

Write down the (fully specified) joint PDF,(,)ofand .

For0< :

,(,)=??

Find([]) .

([])= ??

We do not observe the value of , but are told that=2.2 . Find the MAP estimate ofbased on=2.2 .

MAP estimate of : ??

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