Random Variable $X$ is the number on persons we met til we wrote down every date in a year. Find the expected value of $X$. Find $E(X)$- expected value.
From this example I can definitely understand the true nature of expected value. How do I do this? This is what I tried:
Every date $x_i$ in a year has a $P(x_i)= \frac{1}{365}$on meeting the next person, that's the only useful information I can muster up, and I don't know how to use it. I feel like this is not a easy example.. Any help is well received.
The problem is equivalent to Coupon collector's problem.
The expected value is
$$\mathbb{E}(X) = N H_N \approx N \, ln \, N$$
where $H_N$ is $N$-th harmonic number.
Here $\mathbb{E}(X) \approx 2364.64$
The idea in solving this problem is calculating the expected number of people such that the number of different birthdays we have written increases from $n$ to $n+1$.