2-2-2+离散型随机过程的数字特征

6 5 4 3 2 1
•
• •
x1(t) x2(t)
• •
•
• •
x3(t)
x4(t)
t1
t2
RX (t1 , t2 ) xi (t1 ) xi (t2 ) pii (t1 , t2 )
i 1
4
1 (1 5 2 4 6 2 3 1) 7 4
1/4
6
0 i j pij (t1 , t 2 ) 1 i j 4
•
5 4 3 2 1
• • •
t1
•Hale Waihona Puke Baidu• • •
t2
x1(t) x2(t)
x3(t)
x4(t)
P{ X (t2 ) xi (t2 ) X (t1 ) xi (t1 )} 1 P{ X (t2 ) x j (t2 ) X (t1 ) xi (t1 )} 0
i 1 j 1
4
4
pij (t1 , t2 ) P{ X (t1 ) xi (t1 ), X (t2 ) x j (t2 )} P{ X (t1 ) xi (t1 )}P{ X (t2 ) x j (t2 ) X (t1 ) xi (t1 )}
关键是这个条 件概率的计算
2.2-2 随机过程的数字特征
均值与方差
自相关函数
自协方差函数
离散型随机过程的数字特征
计算举例
离散随机过程的期望值
一般公式 计算举例
1. 一般公式
mX (t ) xi (t ) pi (t )
i 1
2 X N
N
pi (t ) P{ X (t ) xi (t )}
2. 计算举例
例2.2-4： 离散随机过程自相关函数计算 X(t) x1(t) x2 (t) x3 (t) x4 (t) t t1 t2
6
5 4 3 2 1
每一条样本 函数出现的 概率相等
1 5
2 4
6 2
3 1
x1(t) x2(t) x3(t) x4(t)
•
• • •
t1
• • • •
t2
RX (t1 , t2 ) E{ X (t1 ) X (t2 )} xi (t1 ) x j (t2 ) pij (t1 , t2 )
2
(t ) [ xi (t ) mX (t )] pi (t )
i 1
RX (t1 , t 2 ) E{ X (t1 ) X (t 2 )} xi (t1 ) x j (t 2 ) pij (t1 , t 2 )
i 1 j 1
N
N
pij (t1 , t2 ) P{X (t1 ) xi (t1 ), X (t2 ) x j (t2 )}