Unformatted text preview: (6) Suppose X takes the values 0 , 1 , 2 with equal values and U ∼ U (0 , 1) and X ⊥⊥ U . What is the distribution function of X + U ? Does X + U have a density? (7) A post oﬃce has two clerks. Service at clerk i is exp( λ i ) distributed. You arrive and require service but both clerks are busy with one customer each, but apart from these customers there is nobody else in front of you waiting for service. Let T be the amount of time you spend in the post oﬃce until your service is completed. Find E ( T ). 1...
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