Consider the following definition (from here).
A random variable $X$ with finite mean $\mu = \mathbb{E}[X]$ is said to be sub-Gaussian with parameter $\sigma^2$ if: $$\mathbb{E}[e^{\lambda(X - \mu)}] \le e^{\frac{\lambda^2\sigma^2}{2}}.$$
Given this definition, is X sub-Gaussian if it follows a half-normal distribution?