Why is the chi-square distribution skewed to the right and why does it only range from $0$ to $\infty$?

Question

My book says that the chi-squared distribution is continuous, skewed to the right, and ranges from $0$ to $\infty$ with no explanation what-so-ever. It just gives me a table to tell me how to find $P(\chi^2\leq$ some number). So can someone explain to me why chi-squared distribution is continuous, skewed to the right, and ranges from $0$ to $\infty$?

Thank You!

Answer 1

Chi-square distribution is a particular case of Gamma distribution. This should be enough to answer your question.

If not, remember that Chi-square is defined as the sum of squared Standard Gaussian...and thus it must be clear that its range is $[0;+\infty)$.

As skewness is concerned you can calculate it, as usual