An Unexpected Expected-Value Problem, and What Was Wrong With It

It’s such a joy when my daughter asks for help with math. It used to happen all the time; it’s rare now. She just started medical school, and had come home for the weekend to get a quiet space for concentrated study.

“Dad, I have a statistics question.” Be still, my heart!

“It’s asking, if you have a random mRNA sequence with 2000 base pairs, how many times do you expect the stop codon AUG to appear? How do you figure that out?”

I got her to explain enough about messenger RNA so that I could picture this random sequence of 2000 characters, each one A, U, G, or C, and remembered from somewhere that a codon was a chunk of three of these.

“I think it’s more of a probability, or combinatoric question than stats…” I said. (I was wrong about that; interval estimates come up later. Read on.)