Simulation 20191026CSP-S

T1

Stepped pit WARNING! ! !

Each point went to the probability of different (probably several ways to come to the same point), do not go directly to the point of all possible circumstances enumerated directly according to the number of cases and the probability of demand
yesterday T1 also hang, hang today T1 also , then not directly linked T1 live

first a desired conceptual basis:
$E(x)=\sum\limits^n_{i=1}p_i*x_i$among them $p_i$Probability, $x_i$As a result of

Obviously, $x$, $Y$ change two coordinates are independent, so we can consider only one-dimensional
treatment $x^2$ , we find:
$E[x^2]=\frac{\sum\limits^n_{i=0}C^i_n*\sum\limits^i_{j=0}(i-2j)^2}{2^n}$
among them $2^n$ is go $n$ steps all cases, $\sum\limits^n_{i=0}C^i_n$It is to take $i$ -step scheme, $\sum\limits^i_{j=0}(i-2j)^2$ is the result obtained in each pass, $i-2j$ is equivalent to taking the actual displacement (able to walk the walk back acridine $qaq$ )
followed by law of cosines $c^2 = a^2 + b^2 − 2abcosc$provable go $n$ the step is desired $n$ .
Or: go $x$ , the next step must be $x±1$ , in accordance with the desired linear properties, $E(x^2)=E((x±1)^2)=\frac{E((x+1)^2)+E((x-1)^2)}{2}=x^2+1$ , so go $1$ Step contribution to the expectations of all $1$ , and go $n$ the step is desired $n$。