已知离散型随机变量X的可能值为x1= -1,x2= 0,x3=1,且E(X)=0.1,D(X)=0.89,则对应于x1,x2,x3的概率p1,p2,p3为( )A. p1=0.4, p2=0.1, p3 =0.5B. p1=0.1, p2=0.4, p3 =0.5C. p1=0.5, p2=0.1, p3 =0.4D. p1=0.4, p2=0.5, p3 =0.1

步骤 1：列出已知条件
已知离散型随机变量X的可能值为x1= -1, x2= 0, x3=1, 且E(X)=0.1, D(X)=0.89。我们需要找到对应于x1, x2, x3的概率p1, p2, p3。

步骤 2：利用期望公式
E(X) = p1 * x1 + p2 * x2 + p3 * x3
0.1 = p1 * (-1) + p2 * 0 + p3 * 1
0.1 = -p1 + p3
p3 = p1 + 0.1

步骤 3：利用方差公式
D(X) = E(X^2) - [E(X)]^2
E(X^2) = p1 * x1^2 + p2 * x2^2 + p3 * x3^2
E(X^2) = p1 * (-1)^2 + p2 * 0^2 + p3 * 1^2
E(X^2) = p1 + p3
D(X) = p1 + p3 - (0.1)^2
0.89 = p1 + p3 - 0.01
0.9 = p1 + p3
0.9 = p1 + (p1 + 0.1)
0.9 = 2p1 + 0.1
0.8 = 2p1
p1 = 0.4

步骤 4：计算p2和p3
p3 = p1 + 0.1 = 0.4 + 0.1 = 0.5
p1 + p2 + p3 = 1
0.4 + p2 + 0.5 = 1
p2 = 1 - 0.4 - 0.5 = 0.1