Your friend will arrive sometime in the next 3 hours (you have no further inform
ID: 3179613 • Letter: Y
Question
Your friend will arrive sometime in the next 3 hours (you have no further information). Assuming a uniform distribution is appropriate, find the probability he arrives in the last hour, given that he arrived after the first hour.Hint: Let R be the hours till your friends arrival. Then R is distributed as U(0, 3). We want to find P(R > 2 | R > 1)…. Your friend will arrive sometime in the next 3 hours (you have no further information). Assuming a uniform distribution is appropriate, find the probability he arrives in the last hour, given that he arrived after the first hour.
Hint: Let R be the hours till your friends arrival. Then R is distributed as U(0, 3). We want to find P(R > 2 | R > 1)…. Your friend will arrive sometime in the next 3 hours (you have no further information). Assuming a uniform distribution is appropriate, find the probability he arrives in the last hour, given that he arrived after the first hour.
Hint: Let R be the hours till your friends arrival. Then R is distributed as U(0, 3). We want to find P(R > 2 | R > 1)….
Explanation / Answer
here from uniform distribution P(X<x) =x/3
henec P(X>x) =(3-x)/3
hence P(R>2|R>1) =P(R2>2 &R>1)/P(R>!) =P(R>2)/P(R>1) =((3-2)/3)/((3-1)/3) =1/2
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