How does Pierre die? (spoilers)

Let me rephrase my question: why does Nora kill Pierre? (I tried to keep the title as spoiler free as possible.)

In the flashback, they showed Pierre shooting himself. Was this a delusion, a story that Nora wished had happened? So why does she kill him?

To be honest, I wish that Nora didn't do it. The truth taints that very beautiful scene at the hospital where Nora dreamt that he was talking to her.

She's as nervous as a very small nun on a penguin shoot