add a macro for Var, and use it

streaming/streaming.tex

@@ -189,11 +189,11 @@ is $2$-independent). Hence $\E[X_{r, j}] = 1 / 2^r$. By linearity of
 expectation, $\E[Y_{r}] = d / 2^r$.
 
 We will also use the variance of these variables -- note that
-$${\rm Var}[X_{r, j}] \leq \E[X_{r, j}^2] = \E[X_{r, j}] = 1/2^r$$
+$$\Var[X_{r, j}] \leq \E[X_{r, j}^2] = \E[X_{r, j}] = 1/2^r$$
 
 And because $h$ is $2$-independent, the variables $X_{r, j}$ and $X_{r, j'}$
 are independent for $j \neq j'$, and hence:
-$${{\rm Var}}[Y_{r}] = \sum_{j : f_j > 0} {\rm Var}[X_{r, j}] \leq d / 2^r $$
+$$\Var[Y_{r}] = \sum_{j : f_j > 0} \Var[X_{r, j}] \leq d / 2^r $$
 
 Now, let $a$ be the smallest integer such that $2^{a + 1/2} \geq 3d$. Then we
 have:
@@ -208,7 +208,7 @@ $$ \Pr[\hat{d} \leq d / 3] = \Pr[ Y_{b + 1} = 0] \leq
  \Pr[ \vert Y_{b + 1} - \E[Y_{b + 1}] \vert \geq d / 2^{b + 1} ]$$
 
 Using Chebyshev's inequality, we get:
-$$ \Pr[\hat{d} < d / 3] \leq {{\rm Var}[Y_b] \over (d / 2^{b + 1})^2} \leq
+$$ \Pr[\hat{d} < d / 3] \leq {\Var[Y_b] \over (d / 2^{b + 1})^2} \leq
  {2^{b + 1} \over d} \leq {\sqrt{2} \over 3}$$
 
 \qed

tex/adsmac.tex

@@ -170,6 +170,7 @@
 \def\E{{\bb E}}
 \def\Pr{{\rm Pr}\mkern0.5mu}
 \def\Prsub#1{{\rm Pr}_{#1}}
+\def\Var{{\rm Var}\mkern0.5mu}
 
 % Vektory
 \def\t{{\bf t}}