Passengers arrive at a bus station as a Poisson process with rate ?. 1. The only bus departs after a deterministic time T . Let W be the combined waiting time for all passengers. Compute E(W) 2. Now two buses depart, one at T and one at S < T. What is E(W)?
Added by Natalia H.
Close
Step 1
First, we need to find the expected number of passengers arriving during the time T. Since the arrival process is Poisson with rate $\lambda$, the expected number of passengers is $\lambda T$. Show more…
Show all steps
Your feedback will help us improve your experience
Sri K and 70 other Intro Stats / AP Statistics educators are ready to help you.
Ask a new question
Labs
Want to see this concept in action?
Explore this concept interactively to see how it behaves as you change inputs.
Key Concepts
Recommended Videos
Christopher D.
Buses arrive at the station according to a Poisson process at a rate of lambda = 0.4 per minute. Assume at the starting condition is time = 0. Imagine when a bus stops, the probability 1 person gets off at the bus station is p = 0.7, and the probability 2 people get off is p = 0.3, independent of everything else. Let X denote the number of people that get off at the bus station in the first 5 minutes. a) Find E[X] b) Calculate P{X = 2} c) Compute Var(X)
Sri K.
Recommended Textbooks
Elementary Statistics a Step by Step Approach
The Practice of Statistics for AP
Introductory Statistics
Transcript
18,000,000+
Students on Numerade
Trusted by students at 8,000+ universities
Watch the video solution with this free unlock.
EMAIL
PASSWORD