5. Robins and blackbirds make independent visits to a bird feeder. Suppose that the times between visits by robins are given by independent Exponential(2) random variables R₁, R₂, ... and times between visits by blackbirds are given by independent Exponential(2) random variables B₁, B₂, ..., and that more- over these sequences are independent of each other. (a) Show that with probability R/(λR +2B) the first bird to arrive is a robin. Hint: The first bird arrives at time min{R₁, B₁}. (b) Given that n birds have arrived by time t, find and identify the condi- tional distribution for the number of robins that have arrived by time t. Hint: Use the Memoryless Property.

5. Robins and blackbirds make independent visits to a bird feeder. Suppose that the times between visits by robins are given by independent Exponential(2) random variables R₁, R₂, ... and times between visits by blackbirds are given by independent Exponential(2) random variables B₁, B₂, ..., and that more- over these sequences are independent of each other. (a) Show that with probability R/(λR +2B) the first bird to arrive is a robin. Hint: The first bird arrives at time min{R₁, B₁}. (b) Given that n birds have arrived by time t, find and identify the condi- tional distribution for the number of robins that have arrived by time t. Hint: Use the Memoryless Property.

Algebra & Trigonometry with Analytic Geometry

13th Edition

ISBN:9781133382119

Author:Swokowski

Publisher:Swokowski

Chapter10: Sequences, Series, And Probability

Section10.8: Probability

Problem 32E

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