I am doing self-study. but I don`t calculate this problem. so I want to calculating course.
Three numbers are randomly selected and rounded-off to the nearest interger. Let $X_1, X_2, X_3$ denote the round-off errors and assume that they are independent and uniformly distributed over $[-0.4,0.4]$. Let $D$ be the sum of the errors: $D=X_1+X_2+X_3$
1) Compute $E(D)$
2) Compute $\mathrm{Var}(D)$
3) Use the Central Limit Theorem to approximate the probability $P(D>0.1)$. Give the answer in terms of the cdf $\Phi(z)=P(Z<-z)$ of $Z\sim N(0,1)$.