In Problem 10, assume that if a sensor has a choice, it will send the message to
Question:
In Problem 10, assume that if a sensor has a choice, it will send the message to the above sensor with probability pa and will send the message to the sensor to the right with probability pr = 1 −pa. What is the probability that the sensor located at point (10, 5) receives the message?
Problem 10
A wireless sensor grid consists of 21 ×11 = 231 sensor nodes that are located at points (i, j) in the plane such that i ∈ {0, 1,⋯, 20} and j ∈ {0, 1, 2,⋯, 10} as shown in Figure 2.1. The sensor node located at point (0, 0) needs to send a message to a node located at (20, 10). The messages are sent to the destination by going from each sensor to a neighboring sensor located above or to the right. That is, we assume that each node located at point (i, j) will only send messages to the nodes located at (i + 1, j) or (i, j + 1). How many different paths do exist for sending the message from node (0, 0) to node (20, 10)?
Step by Step Answer:
Introduction To Probability Statistics And Random Processes
ISBN: 9780990637202
1st Edition
Authors: Hossein Pishro-Nik