# Homework Help: Distribution of Log of Variance

1. Nov 12, 2013

### Yagoda

1. The problem statement, all variables and given/known data
If $Y_1, Y_2, ...$ are iid with cdf $F_Y$ find a large sample approximation for the distribution of $\log(S^2_N)$, where $S^2_N$ is the sample variance.

2. Relevant equations

3. The attempt at a solution
The law of large numbers states that for large N $S^2_N$ converges in probability to $\sigma^2$. However, because I don't know the distribution of the Y's I don't know what $\sigma^2$ is.

Also $\log S^2_N = \log(\frac{1}{N} \sum_{i=1}^{N} (Y_i - \mu) ^2) = \log(\frac{1}{N}) + \log(\sum_{i=1}^{N} (Y_i - \mu) ^2)$, but I am not sure if this helps me find an approximation for the distribution.