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In this problem, we're looking at a two stage process in which the first stage, we roll a fair die which has four faces to obtain a number N, where N belongs to the set 0, 1, 2, and 3 with equal probability. Now, given the result of the die roll, N will toss a fair coin N times in getting K heads from the coin tosses. For instance, if from the first die roll, we get N equal to 3, then we'll toss a coin 3 times. Let's say the outcome is heads, heads, and tails. And that will give us K equal to 2. For part A, we're asked to compute the PMF for N, which is a result of the first die roll. Now, since we had assumed the die roll was uniformly distributed in the set in the set 0, 1, 2, and 3, we have that the chance of N being equal to any little n is equal to 1/4 if n is in the set 0, 1, 2, 3, and 0 otherwise. If we were to plot this in a figure, we'll have the following plot. For part B, things are getting a little more complicated. This time, we want...

Let's finish up by looking at two extended examples. The scenario for both examples is the control system for the International Space Station, which has to handle three recurring tasks: supply ship guidance (SSG), gyroscope control (G), and cabin pressure (CP). For each device, the table shows us the time between successive requests (the period), the service time for each request, and the service deadline for each request. We'll first analyze the system assuming that it's using a weak priority system. First question: What is the maximum service time for the cabin pressure task that still allows all constraints to be met? Well, the SSG task has a maximum allowable latency of 20 ms, i.e., it's service routine must start execution within 20 ms if it is to meet its 25 ms deadline. The G task has a maximum allowable latency of 10 ms if it's to meet its deadline. So no other handler can take longer than 10 ms to run or the G task will miss its deadline. 2. G...