I don't know if this has been covered by other posts since those posts mention things like "Brownian motion" and "martingales", while I'm literally just in the beginning of learning this stuff.
Anyway, I have 2 questions about the material in these lecture notes that I found online. https://web.ma.utexas.edu/users/gordanz/notes/lecture4.pdf
1) Notation.
A sequence:
$ \{{X_n}\}_{n \in N_0}$
I want to verify that my understanding of the above is correct. If the above is a sequence of random variables with parameter $p \in (0,1)$, does that mean that each X is an array of 0 and 1's. or is each X a single 0 or 1, but TOGETHER $X_1$, $X_2$ $X_3$... $X_n$ make up that sequence?
2) On page 2 of the lecture notes, it mentions "running maximum processes". Even though the proof for the probability mass function is right there in those notes, I can't understand it. Why does
$p_1 = P[M_n=l]=P[M_n=l]+P[M_n=l+1]$
include the $P[M_n=l+1]$ part?
3) Finally, do you recommend any resources for me to learn this stuff? I'm slowly using lecture notes written by professors at universities, but I find it sometimes too abstract (sorry, I'm too dumb).
Thanks.