Can chi-squared distribution be left-skewed? I'm learning chi-squared distribution and know that as degree of freedom increases, right-skewed chi-squared distribution will approximate to normal distribution shape. I'm wondering can its distribution become left-skewed? How should I approach to think about this question?
Thanks.

No, the skewness of the chi-squared distribution with $k$ degrees-of-freedom is:
$$\mathbb{Skew} = \sqrt{\frac{8}{k}},$$
which is positive for all $k > 0$.  The distribution is asymptotically unskewed as $k \rightarrow \infty$, and indeed, in this case it converges to the normal distribution (in an appropriately standardised sense).
