Skip to content

Commit

Permalink
Update 5-1.md
Browse files Browse the repository at this point in the history
As we want to compute the variance of V_n, it will be decomposed to X_1, \cdots X_n instead of V_1, \cdots, V_n, so this typo is actually quite apparent.
  • Loading branch information
ichn-hu authored and walkccc committed Mar 21, 2019
1 parent 3c671cb commit edad753
Showing 1 changed file with 1 addition and 1 deletion.
2 changes: 1 addition & 1 deletion docs/Chap05/Problems/5-1.md
Original file line number Diff line number Diff line change
Expand Up @@ -82,7 +82,7 @@ Why is the second way more rigorous than the first? Both ways condition on the v

**b.** Defining $V_n$ and $X_j$ as in part (a), we want to compute $\text{Var}[V_n]$, where $n_i = 100i$. The $X_j$ are pairwise independent, and so by equation $\text{(C.29)}$,

$$\text{Var[$V_1$]} + \text{Var[$V_2$]} + \cdots + \text{Var[$V_n$]}.$$
$$\text{Var[$V_n$]} = \text{Var[$X_1$]} + \text{Var[$X_2$]} + \cdots + \text{Var[$X_n$]}.$$

Since $n_i = 100i$, we see that $n_{i + 1} - n_i = 100(i + 1) - 100i = 100$. Therefore, with probability $99 / 100$, the increase in the value represented by the counter due to the $j$th $\text{INCREMENT}$ operation is $0$, and with probability $1 / 100$, the value represented increases by $100$. Thus, by equation $\text{(C.27)}$,

Expand Down

0 comments on commit edad753

Please sign in to comment.