How much does a typical biologist know about signal processing, machine learning, and (theoretical) computer science?
I don't know what a "typical" biologist is, but I'd guess they don't know much about computers, because the population in general is computer illiterate. In my department, we do have a lab that does a lot of computational work on proteins. And of course bioinformatics relies on computers. 

I can see where programming would come in handy for an ecologist, and maybe hardware and electronics too. Lets say you want to track animals in the woods. Traditionally, you'd give them a radio collar, then you'd have to triangulate their position in the woods, and at the end of the day all you'd have is location data. You could use something like a Raspberry Pi or Arduino to create a device that has GPS, a camera, and cell phone antenna, which could record much more information about the animal's location and activity and send it back you without as much effort.

In our modern computerized age, knowing some programming is always a plus, no matter what field you're in. Finding ways to apply that skill aren't always easy. I know both Java and C++, but I've really only written a few programs that I've used in research, 1 to calculate number of possible peptides given a size and some amino acids that won't change, and one to calculate how much DNA to use in ligation reactions.