To justify whether or not jointly Gaussian

Question

Let $X_{1}$,..., $X_{n}$ be random variables, and define $$Y_{k} := \sum_{i=1}^{k} X_{i}, k = 1,...,n.$$ Suppose that $Y_{1}$,..., $Y_{n}$ are jointly Gaussian. Determine whether or not $X_{1}$,...,$X_{n}$ are jointly Gaussian.

I do not know how to solve it!

Answer 1

$(X_1,X_2,...,X_n)=(Y_1,Y_2-Y_1,...,Y_n-Y_{n-1})$. This implies that $X_i$'s are jointly Gaussian.