This post covers Introduction to probability from Statistics for Engineers and Scientists by William Navidi.

Exercises

• A mobile ad hoc computer network consists of several computers (nodes) that move within a network area. Often messages are sent from one node to another. When the receiving node is out of range, the message must be sent to a nearby node, which then forwards it from node to node along a routing path toward its destination. We wish to predict the proportion of messages that will be successfully delivered, which is called the goodput.

  It is known that the goodput is affected by the average node speed and by the length of time that the nodes pause at each destination. Below table presents average node speed, average pause time, and goodput for 25 simulated mobile ad hoc networks.

• Use the multiple regression model to predict the goodput for a network with speed

  12 m/s and pause time 25 s.

• For the goodput data, find the residual for the point Speed = 20, Pause = 30.

• Find a 95% confidence interval for the coefficient of Speed in the multiple regression

  model.

• Test the null hypothesis that the coefficient of Pause is less than or equal to 0.3.

• Find a 95% confidence interval for the mean response 𝜇yi , and a 95% prediction

  interval for a future observation when Speed = 25 and Pause = 15.