Lecture examples vs homeworks

{$\cal J$} asks why the examples that I cover in the lectures are harder than homeworks?

It would be easy to say that you're working so hard trying to understand my lectures that the homeworks just seem easy (i.e., you're smarter than you think you are). However, I resist....

More seriously, probability is hard. However, it is also important for computer engineering. I worry that omitting assorted topics will make it harder for you in later courses.

Being able to analyze things properly in the real world is useful because assorted expensive engineering mistakes, sometimes resulting in innocent people dieing in gruesome ways, have resulted from errors. Luckily the only RPI grad I can think of who did this was Cooper, chief architect of the Quebec bridge, in 1907.

Therefore I don't apologize for keeping the course level high. The School of Engineering is the best school at RPI, e.g., in national rankings. That didn't happen accidentally.

All that said, if you do an honest amount of work, you should get a fair reward. Therefore, the homeworks and exams are easier. If you do well on them, you will get a reasonable grade.

Still more Chapter 5 examples

It's important to understand chapter 5.

1. Example 5.30 p263. # defects in a region; random splitting of Poisson counts.
2. Example 5.36 p269. Average # defects in a region.
3. Example 5.35 p268. Maximum a posteriori receiver. Here, we are using our analysis to design the best receiver. Using probability to optimize a design is common.
4. Example 5.37 p268. Mean for binary channel.
5. Example 5.46 p281. Most likely conditional rainfall for joint Gaussian r.v. We are using probability to infer the most likely value for one number, given some observation. E.g., suppose a weather station burnt down, so we're missing an observation. However, we have its historical records, and also those of the other stations, so what's the best guess for the missing observations?
6. Example 5.47 p282. We observe a noisy analog signal. What's the most likely signal?