Recent content by devonho

Homework Statement Let there be two discrete random variables: X \in \lbrace 1,2,3,4,5,6,7,8,9,10 \rbrace \quad \text{where } P[X] \text{ is uniformly distributed over the sample space of } X \text{.} B = \left\lbrace \begin{array}{cl} 1 & \text{if} \quad X>4 \\ 0 &...

This seems to work: {\bf r}= \left[ \begin{array}{ccccc} r_1 & 0 & \ldots & & 0\\ 0 & r_2 & & & \vdots \\ \vdots & & r_3 & & \\ & & & \ddots & \\ 0 & \ldots & & & r_n \\ \end{array} \right] {\bf e}= \left[ \begin{array}{c} e_1 \\ e_2 \\ \vdots\\...

Homework Statement Given vectors {\bf r}=\left[r_1,r_2,r_3\ldots{}r_n\right]^T {\bf e}=\left[e_1,e_2,e_3\ldots{}e_n\right]^T I need to write the sum \sum_{i=1}^{n}r_ie_i^2 in terms of {\bf r} and {\bf e} Homework Equations Nil. The Attempt at a Solution Without...

Hi SammyS, {\bf x}{\bf x}^T is 3x3 while {\bf x}^T{\bf x} is 1x1

Homework Statement Hi, Is there a matrix property that can be applied to take the square of a column vector? Something like: {\bf x}=\left[x_1,x_2,x_3\right]^T \left[{\bf x}\right]^2 ={\bf x}{\bf x}^T or ={\bf x}^T{\bf x}? Thank you. Homework Equations The...

Thanks for the help. I wrote the long proof. If m_{12}=m_{21}, m_{13}=m_{31},m_{32}=m_{23}, \bf{x} = \left[ \begin{array}{ccc} x_1 \\ x_2 \\ x_3 \end{array} \right] \bf{y} = \left[ \begin{array}{ccc} y_1 \\ y_2 \\ y_3 \end{array} \right] \bf{M} = \left[...

Hi all, thanks for the replies. The goal was to get: (\bf{x-\mu_{i}})^{t}\Sigma^{-1}(\bf{x-\mu_{i}}) = \bf{x}^t\Sigma^{-1}\bf{x}+ \bf{\mu_{i}}^t\Sigma^{-1}\bf{\mu_{i}}- 2\bf{x}^t\Sigma^{-1}\bf{\mu_{i}} Hence, \bf{\mu_i}^t \Sigma^{-1} \bf{x} = \bf{x}^t \Sigma^{-1} \bf{\mu_i} Was...

Homework Statement I need help with expanding: (\bf{x-\mu_{i}})^{t}\Sigma^{-1}(\bf{x-\mu_{i}}) \bf{x,\mu_{i}} are column vectors. \Sigma is a square matrix. Thank you. Homework Equations Can: \bf{x}^t\Sigma^{-1}\bf{\mu_{i}} be written as...