# Probability density function

$$f(x)=(2pi)^{-n/2}e^{frac{-sum_{i=1}^nx_i^{2}}{2}}$$ $$times$$ ($$1$$ + $$Pi_{i=1}^nx_ie^{frac{-x_i^{2}}{2}}$$)

$$Xin$$ $$mathbb{R^{n}}$$ Is this multivariate normal?
Does $$(X_1, X_2,…, X_n)^{T}$$ have a multivariate normal distribution?