Homework IV

Due Thursday, November 18.

Problem 1:

This is Problem A of Hwk V for ECS 132.

Problem 2:

Consider a random walk on the integers, -∞ to ∞, with holding times at each position being exponentially distributed with parameter λ. We start at 0.

1. Find, as an expression in λ, the probability that at time t we are at state i. This must be evaluatable by any calculus student, if they are provided a value of λ. It is OK to have an infinite series in the expression, without knowing how to sum it.
2. Use R to plot this probability for a range i = 0,1,...,c, for reasonable values of c and t of your choice.
3. Confirm your answer via R simulation.

Problem 3:

Consider the disk file model on p.356. Here we will assume that file size is uniformly distributed on (0,1), rather than (0,3).

1. Find the long-run proportion of files that are split between two tracks.
2. Find the long-run proportion of tracks that contain exactly two files. (These are necessarily partial files.)
3. Confirm both results above via R simulation.