I'm going to repost this here since my questions never get answered on mathstackexchange. It might be better suited to this location, as well.
At the end of the workday, I add an amount between 0 and 1 dollar to my change container. The amount added is standard uniform (unif(0,1)) and each day's amount is independent.
However, last night I took all my change to the bank, setting my total in the container back to $0. Such a "bank trip" happens as a Poisson process with a rate of 5 per year.
What is the expected number of days before I have 1 dollar?
What is the expected total amount of money I will have the morning after I have first reached 1 dollar?
What's the probability I'll never get over $10 in a year?
I'm really not sure how to formulate this. I know the sum of n iid standard uniform variables has mean n/2, so I would expect two days for part (a). But that doesn't take into account the poisson process....
(b) and (c) I have no idea. I suppose it depends on how I solve part (a). My background in Poisson Processes is pretty weak. This is outside of coursework, so please don't feel bad about "handholding" and guiding me to the solution. Thank you for any help.
