Future Lifetime Distribution Suppose the future lifetime of someone aged $20$ denoted by $T_{20}$ is subject to the force of mortality $\mu_x = \frac{1}{100-x}$ for $x< 100$. What is $\text{Var}[\min(T_{20},50)]$?
So we have: $$E[\min(T_x,50)|T_{20} > 50] = 50$$ $$\text{Var}[\min(T_{20},50)|T_{20} > 50] = ?$$ $$E[\min(T_x,50)|T_{20} \leq 50] = 25$$ $$\text{Var}[\min(T_{20},50)|T_{20} \leq 50] = 50^{2}/12$$ 
What is the second line?
Also I know that we use the "expectation-variance" formula to calculate $\text{Var}[\min(T_{20},50)]$.

Hint: The random variable $\min(T_{20},50)|T_{20} > 50)$ doesn't vary much!
If you then want to use a formula, call the above random variable $Y$. We want $E((Y-50)^2)$. How did you decide earlier that $E(Y)=50$?
