Construct finite independent sums and compare repeated copies with scaling
A finite random variable X has the following distribution. The variables X₁,...,Xₙ are mutually independent and each has exactly this distribution
| \(x\) | \(\Pr(X=x)\) |
|---|---|
| \(-1\) | \(\frac{4}{5}\) |
| \(2\) | \(\frac{1}{5}\) |
\[n=2,\qquad S_n=X_1+\cdots+X_n\]