Dispatches to the Miami Coast Guard Search & Rescue Division concern either routine or emergency cases. The time to process a routine case is an exponential random variable with an expected value of 3 minutes, while the time to process an emergency case is an exponential random variable with an expected value of 10 minutes. A dispatch is routine with a probability of 0.8, or an emergency with a probability of 0.2. The status of dispatches and processing times are independent across dispatches. Let X be the processing time of the next dispatch. a) Calculate P{X > 4}. b) Calculate E[X]. c) Calculate Var(X). (Hint: Var(X) = E[Var(X |Y )] + Var(E[X |Y ]).

Dispatches to the Miami Coast Guard Search & Rescue Division concern either routine or emergency cases. The time to process a routine case is an exponential random variable with an expected value of 3 minutes, while the time to process an emergency case is an exponential random variable with an expected value of 10 minutes. A dispatch is routine with a probability of 0.8, or an emergency with a probability of 0.2. The status of dispatches and processing times are independent across dispatches. Let X be the processing time of the next dispatch. a) Calculate P{X > 4}. b) Calculate E[X]. c) Calculate Var(X). (Hint: Var(X) = E[Var(X |Y )] + Var(E[X |Y ]).

A First Course in Probability (10th Edition)

10th Edition

ISBN:9780134753119

Author:Sheldon Ross

Publisher:Sheldon Ross

Chapter1: Combinatorial Analysis

Section: Chapter Questions

Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...

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A dispatch is routine with a probability of 0.8, or an emergency with a probability of 0.2.

The status of dispatches and processing times are independent across dispatches.

Let X be the processing time of the next dispatch.

a) Calculate P{X > 4}.
b) Calculate E[X].
c) Calculate Var(X). (Hint: Var(X) = E[Var(X |Y )] + Var(E[X |Y ]).

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