Math & Science ⇒ Sigmas in equations and align

[Sjj177]

Hello.

I am summarizing some theory and now I've got the following code

Code: Select all

{\bf Theorem 4.3} If $c_1, c_2,\ldots,$ and $c_n$ are constants, then
\begin{equation*}
E\begin{bmatrix}
\sum\limits_{i=1}^{n}c_ig_i(X)
\end{bmatrix} = \sum\limits_{i=1}^{n}c_iE[g_i(X)]
\end{equation*}
{\bf{\textit{Proof}}} According to Theorem 4.1 with $g(X) = \sum\limits_{i=1}^{n}c_ig_i(X),$ we get
\begin{align*}
E\begin{bmatrix}
\sum\limits_{i=1}^{n}c_ig_i(X)
\end{bmatrix}
&=\sum\limits_x
\begin{bmatrix}
\sum\limits_{i=1}^{n}c_ig_i(X)
\end{bmatrix}
f(x)\\
&= \sum\limits_{i=1}^{n}\sum\limits_{x}c_ig_i(x)f(x)\\
&= \sum\limits_{i=1}^{n}c_i\sum\limits_{x}g_i(x)f(x)\\
&= \sum\limits_{i=1}^{n}c_iE[g_i(X)]
\end{align*}

My problem here is that the sigmas in the "brackets" are smaller than the others. Does anybody know how to fix this?

[Sjj177]

Okay never mind, next time I will have to think harder before I actually ask something xD... solved it... (should take my hands of those matrices..) For the ones interested (with the same question for example), I solved it this way:

Code: Select all

{\bf Theorem 4.3} If $c_1, c_2,\ldots,$ and $c_n$ are constants, then
\begin{equation*}
E\left[
\sum\limits_{i=1}^{n}c_ig_i(X)\right]
 = \sum\limits_{i=1}^{n}c_iE[g_i(X)]
\end{equation*}
{\bf{\textit{Proof}}} According to Theorem 4.1 with $g(X) = \sum\limits_{i=1}^{n}c_ig_i(X),$ we get
\begin{align*}
E\left[
\sum\limits_{i=1}^{n}c_ig_i(X)
\right]
&=\sum\limits_x
\left[
\sum\limits_{i=1}^{n}c_ig_i(X)
\right]
f(x)\\
&= \sum\limits_{i=1}^{n}\sum\limits_{x}c_ig_i(x)f(x)\\
&= \sum\limits_{i=1}^{n}c_i\sum\limits_{x}g_i(x)f(x)\\
&= \sum\limits_{i=1}^{n}c_iE[g_i(X)]
\end{align*}