What is the relationship between a chi-square distribution and a normal distribution?

Question

I am wondering what is the correlation between a chi-squared distribution and normal distribution.

For example, considering if x~N(mu, sigma), does that mean x^2~chi-square distribution?

Thank you every much for your time.

Answer 1

The relation between them is that if $Z_1,...,Z_n$ are i.i.d standard normal random variables, $Z_i \sim N(0, 1)$, and if $$Y = \sum_i^nZ_i^2$$ Then $Y$ follows a Chi-squared distribution with $n$ degrees of freedom
$$Y \sim \chi_{n}^2$$