Variance of sum of $10$ random variables. Find the variance of sum of $10$ random variables if each has variance $5$ and if each pair has a correlation coefficient $.5$
Let $Y=X_1+X_2+X_3+\ldots+X_{10}$
I tried this problem by calculating variance of first $10$  random variables.
$V(Y)=50$. Then there will be $45$ pairs of covariance terms. 
Correlation coefficient $\rho=.5$ 
$Cov(X_i,X_j)=2.5 $
Which  gives variance $V(Y)=50+2.5=52.5$
Did i do everything right, please someone tell me.

$$Y=\sum_{n=1}^{10}X_n\to var(Y)=E(Y^2)-E^2(Y)\\=E(\sum_{n=1}^{10}X^2_n+\sum_{m,n=1\\m\ne n}^{10}X_nX_m)-(\sum_{n=1}^{10}E(X_n))^2\\=50+90\times 2.5-(\sum_{n=1}^{10}E(X_n))^2$$if we take $E(X_n)=0$ we will have:$$var(Y)=275$$
