probability and expectation without replacement From a box containing N identical tickets numbered 1 to N, n tickets are drawn without replacement. Let X be the largest number drawn. Find E[X]
I got the pdf as x-1Cn-1/NCn
And E(X)=summation x*pdf
Here i am stuck and i dont know whether what i have done is right or no

Hints:


*

*$\mathbb EX=P(X\geq1)+\dots+P(X\geq N)$

*$P(X\geq k+1)+P(X\leq k)=1$



edit:
$$\mathbb{E}X=\sum_{i=1}^{N}ip_{i}=\sum_{i=1}^{N}\sum_{k=1}^{i}p_{i}=\sum_{k=1}^{N}\sum_{i=k}^{N}p_{i}=\sum_{k=1}^{N}P\left(X\geq k\right)=$$$$\sum_{k=1}^{N}\left(1-P\left(X\leq k-1\right)\right)=N-\sum_{k=1}^{N}P\left(X\leq k-1\right)=N-\sum_{k=n}^{N-1}P\left(X\leq k\right)$$
and for $k\in\{n,n+1,\dots,N\}$:
$$P(X\leq k)=\frac{\binom{k}{n}}{\binom{N}{n}}$$
