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 and Trigonometry (MindTap Course List)

4th Edition

ISBN:9781305071742

Author:James Stewart, Lothar Redlin, Saleem Watson

Publisher:James Stewart, Lothar Redlin, Saleem Watson

Chapter14: Counting And Probability

Section14.2: Probability

Problem 3E: The conditional probability of E given that F occurs is P(EF)=___________. So in rolling a die the...

See similar textbooks