In the answer for the following exercise:
Let $\{x_1,...,x_n\}$ be a finite collection of random variables with $E(x_i^2) \lt \infty$ ($i = 1,..., n$). Show that the set of all linear combinations $\Sigma_{i=1}^{n} \alpha_i x_i$ constitutes a vector space, which we denote by $L^\dagger_2$,
there's a statement that I don't really understand, that is:
The difficulty is that a random variable $y = \Sigma_{i}\alpha_i x_i$ might also be expressible as $y = \Sigma_{i}\beta_i x_i$, where $(\alpha_1,...,\alpha_n) \ne (\beta_1,...,\beta_n)$.
For simplicity, suppose that $n=2$ so we have only two random variables $x_1$ and $x_2$ in the collection. How could I construct an example where $y=\alpha_1 x_1 + \alpha_2 x_2=\beta_1 x_1 + \beta_2 x_2$ where $(\alpha_1, \alpha_2)\ne (\beta_1, \beta_2)$?