Currently going through solutions of a worksheet and I don't understand the jump between two lines of working.
"$\hat{\theta}_1$ and $\hat{\theta}_2$ are independent unbiased estimators for an unknown parameter $\theta$, with respective variances ${\sigma}_1^2$ and ${\sigma}_2^2$. Show that $\hat{\theta}_3 = \lambda\hat{\theta}_1 + (1 − \lambda)\hat{\theta}_2$ is also an unbiased estimator of $\theta$ for all values of $\lambda$"
This is straightforward and gave me no problems, I have included it in case it is relevant for the next part
"Calculate the variance of $\hat{\theta}_3$"
The solution given is
Var[$\hat{\theta}_3$] $= {\lambda}^2$Var[$\hat{\theta}_1$]$+(1−λ)^2$Var[$\hat{\theta}_2$]
$= {\lambda}^2{\sigma}^2_1+ {(1 − \lambda)}^2{\sigma}^2_2$
$= \theta$
The part which I don't understand is how ${\lambda}^2{\sigma}^2_1+ {(1 − \lambda)}^2{\sigma}^2_2 = \theta$. Any help would be appreciated.