Cannot find module ‘rxjs-compat/Observable’

None of these answers are correct.
Installing rxjs-compat is just a workaround. All you have to do is correct the imports. Use:

import { Observable } from 'rxjs';

Instead of:

import { Observable } from 'rxjs/Observable';

This last import is supposed to go away when they finally decide to kill rxjs-compat (hopefully very soon)… so heads up! you need to update your code!!