Proof | Property of Covariance
Proof \begin{eqnarray*}Cov[X, Y]&=&E[(X-E[X])(Y-E[Y])]\\&=&E[XY–XE[Y]-E[X]Y+E[X]E[Y]]\\& […]
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Proof \begin{eqnarray*}Cov[X, Y]&=&E[(X-E[X])(Y-E[Y])]\\&=&E[XY–XE[Y]-E[X]Y+E[X]E[Y]]\\& […]
もっと読む →Proof : Let X be a random variable and a be any constant. \begin{eqnarray*}V[aX]&=&E[\left(aX-E[aX]\ri […]
もっと読む →Proof : Let a be any constant. \begin{eqnarray*}V[a]&=&E[\left(a-E[a]\right)^{2}]\\&=&E[(a-a)^ […]
もっと読む →\begin{eqnarray*}V[X]&=&E[\left(X-E[X]\right)^{2}]\\&=&E[X^{2}-2E[X]\cdot X+\{E[X]^{2}\}]\\&am […]
もっと読む →Let X be a random variable. Then the variance and standard deviation of X are defined by $$\text{Variance : } […]
もっと読む →Let X be a random variable. Then the expectation of X is defined by \begin{eqnarray*}E[X]&=&\sum_{x}\ […]
もっと読む →Let A and B be events such that P(A)>0. We denote the probability of B given that A has occurred by $$P(B|A […]
もっと読む →Suppose that X can take any one of n values and Y can take any one of m values . Then the probability of the e […]
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