题目
1.设随机变量X与Y的联合分布律为-|||-Y-|||-X -1 0 2-|||--1 dfrac (1)(6) dfrac (1)(12) 0-|||-0 dfrac (1)(4) 0 0-|||-1 dfrac (1)(12) dfrac (1)(4) dfrac (1)(6)-|||-试求(1) (X-Y), E(XY);-|||-(2).cov(X,Y)与 (X-2Y);-|||-(3)ρ(X,Y).
题目解答
答案
解析
步骤 1：计算E(X-Y)
E(X-Y) = E(X) - E(Y)
E(X) = $\sum_{x} x \cdot P(X=x)$
E(Y) = $\sum_{y} y \cdot P(Y=y)$
步骤 2：计算E(XY)
E(XY) = $\sum_{x,y} xy \cdot P(X=x, Y=y)$
步骤 3：计算cov(X,Y)
cov(X,Y) = E(XY) - E(X)E(Y)
步骤 4：计算D(X-2Y)
D(X-2Y) = E[(X-2Y)^2] - [E(X-2Y)]^2
步骤 5：计算ρ(x,Y)
ρ(x,Y) = cov(X,Y) / [√D(X) * √D(Y)]
E(X-Y) = E(X) - E(Y)
E(X) = $\sum_{x} x \cdot P(X=x)$
E(Y) = $\sum_{y} y \cdot P(Y=y)$
步骤 2：计算E(XY)
E(XY) = $\sum_{x,y} xy \cdot P(X=x, Y=y)$
步骤 3：计算cov(X,Y)
cov(X,Y) = E(XY) - E(X)E(Y)
步骤 4：计算D(X-2Y)
D(X-2Y) = E[(X-2Y)^2] - [E(X-2Y)]^2
步骤 5：计算ρ(x,Y)
ρ(x,Y) = cov(X,Y) / [√D(X) * √D(Y)]