Probability and Statistics Question

[PhysViti]

Homework Statement

It's problem 1. (b) in the attachment. I need help finding the average number of records.

Note: Obviously, I'm not actually in the class. I just got bored and started going through the course assignments

Homework Equations

From the first part of the question, I know that:

$$P_n= \frac {1}{n}$$

I also know that if f(n) is the probability of there being n records, then:

$$<S_N> = \sum_{n=1}^{N} f(n)n$$

The Attempt at a Solution

I know that the answer is supposed to be:

$$<S_N>=\sum_{n=1}^{N} P_n$$

I'm not sure how to derive this. I know that I need to find f(n) first, but all the ways I can think of finding it are extremely complicated. I think finding <S_n> is supposed to be easy, since in the solutions the answer is written down without any explanation.

 

[PhysViti]

Never mind, I figured it out.

 

[Dick]

It's just the definition of an expectation value. You have a probability of 1/n of getting 1 record in each of N trials. Total expectation is the sum 1*(1/n). You definitely don't want to try and break it down like that. Finding f(n) IS complicated.