Professor de la Pena's class was the worst academic experience I've had at Columbia. As (I hope) several other engineering students will attest, it was not the lack of basic math skills that caused the majority of this class to get stuck during lectures and problem sets. But don't assume the only problem was the A math major in the class told me before the final that he was lost too.
Yes, Professor de la Pena is a nice person - he really *wishes* the class would understand what he's talking about, and he tries to help, but he's just not effective in conveying the material. He was so nice that when he realized that most of the class didn't understand what was going on, he made the midterm take-home. (Several students broke their agreement to work individually, resulting in a "binormal" distribution, with a mean in the 60s and another small cluster in the 90s. Otherwise there would have been very few high scores - on a straightforward take-home exam!)
That brings us to the nature and content of the class. It's called "Probability Models" but should be called "Probability Theory." It's not very practical for scientists and engineers; we went over the derivations for a few of models, but didn't really get into their applications. The lectures were very theory-oriented, and he assumed a better background in theory than most students had. During an extra-credit presentation (another "nice" addition to the class), a student explained how one could use a "lemma" to build a proof, and noted that he/she had never heard of a lemma before. The class laughed, because Professor de la Pena had used the word in several lectures without explaining what it meant (it's a statement that's been proven already).
We didn't get to important concepts like covariance and correlation-the very foundation of statistical scientific methods.
The books are near-worthless (but cost a combined $250). Find a different book to learn from if you have to take this class.
But don't take this class with de la Pena. Petition your department to change the requirement, take it during the summer at a state college, or even take a more advanced class (this class had no calc IV requirement, though you needed double integrals).
If you have a good resource to learn from, I guess you could do well in this class. I haven't received my grade, so I don't know if it's true that he curves to an A-. That would be nice, but I don't feel like I learned statistics.