设随机变量X的期望为E(x),方差为D(x)>0,X*=(X-E(x))/根号下D(x),求E(X*),D(X*)
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设随机变量X的期望为E(x),方差为D(x)>0,X*=(X-E(x))/根号下D(x),求E(X*),D(X*)
![设随机变量X的期望为E(x),方差为D(x)>0,X*=(X-E(x))/根号下D(x),求E(X*),D(X*)](/uploads/image/z/17897058-18-8.jpg?t=%E8%AE%BE%E9%9A%8F%E6%9C%BA%E5%8F%98%E9%87%8FX%E7%9A%84%E6%9C%9F%E6%9C%9B%E4%B8%BAE%28x%29%2C%E6%96%B9%E5%B7%AE%E4%B8%BAD%28x%29%3E0%2CX%2A%3D%28X-E%28x%29%29%2F%E6%A0%B9%E5%8F%B7%E4%B8%8BD%28x%29%2C%E6%B1%82E%28X%2A%29%2CD%28X%2A%29)
E(X*) = E[(X-E(X))/√D(X)] = [E(X)-E(X)]/√D(X) = 0
D(X*) = E{[X*-E(X*)]^2} = E{[(X-E(x))/√D(x)]^2}
= E[X-E(x)]^2] / D(X)
= D(X)/D(X)
= 1
因此随机变量X*的数学期望E(X*) = 0,方差D(X*) = 1.
D(X*) = E{[X*-E(X*)]^2} = E{[(X-E(x))/√D(x)]^2}
= E[X-E(x)]^2] / D(X)
= D(X)/D(X)
= 1
因此随机变量X*的数学期望E(X*) = 0,方差D(X*) = 1.
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