Proof | Properties of Variance (3)
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 →Welcome to Math World!
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 →A complex number can be represented by an expression of the form where and are real numbers and is a symbol wi […]
もっと読む →We can see that and are one-to-one, so they have inverse functions denoted by and . However, is not one-to-one […]
もっと読む →Proof Let . Then by the definition of inverse functions, $$x=\sinh y=\frac{e^{y}-e^{-y}}{2}$$ so multiplying b […]
もっと読む →Let and . Then the point lies on the right branch of the hyperbola since and . For your reference, recall that […]
もっと読む →An equation of the tangent plane to the surface at the point is given by $$z-z_{0}=f_{x}(x_{0},y_{0})(x-x_{0}) […]
もっと読む →A square root of a number is a number x such that . Calculation Formula Example:
もっと読む →Notice that two nonzero vectors and are parallel if and only if or . In either case , so and therefore . Thus, […]
もっと読む →The cross product is defined only when the cross product and are 3-dimensional vectors. Note that the cross pr […]
もっと読む →