# Demonstration for covariance with linear combination of 2 variables

I don't know how to prove this relation :

I know that : $$\text{Var}\bigg(\sum_{i}\,a_{i}\,X_{i}\bigg)=\sum_{i}a_{i}^{2}\,\text{Var}(X_{i})+\sum_{1\leq i \leq j\leq n} 2\,a_{i}a_{j}\text{Cov}(X_{i},X_{j})$$

But I don't know how to use this relation to get the final relation above concerning the term $$\text{cov}(Y_{1},Y_{2})$$

If someone could help me, this would be nice. Regards

• Independence is not in the hypothesis so the equation for the variance is not correct. – Kavi Rama Murthy Feb 3 at 0:45
• @KaviRamaMurthy . Sorry, I forgot the covariance term – youpilat13 Feb 3 at 0:49