Update 4.md

updated equation in line 15

_problems/unit-05/properties-of-estimators/4.md

@@ -12,7 +12,7 @@ statement: |
 ---
 The converse statement is false. For a counterexample, let each $X_i$ be discrete with pmf,
 
-$$f_i = \begin{cases}1-\frac{1}{i}, & x=0\\ 
+$$f_i = \begin{cases}1-\frac{1}{i}, & x=0 \\ 
 \frac{1}{2i}, &x \in \{-i, i \}\\ 
 0, &\text{otherwise} \end{cases}$$
 
@@ -22,4 +22,4 @@ We can also compute,
 
 $$V[X_i] = E[ (X_i - 0)^2 ] = E[X_i^2] = \sum_{x \in Supp[X_i]} x^2 f_i(x) = (-i)^2 \frac{1}{2i} + (0)^2(1 - \frac{1}{i}) + (i)^2 \frac{1}{2i}  = \frac{i}{2}$$
 
-Hence, as $i \to \infty$, $V[X_i] \to \infty$, not to zero as required by the statement.
+Hence, as $i \to \infty$, $V[X_i] \to \infty$, not to zero as required by the statement.