1.  "relative to its average"

2.  checking whether the (sample) mean and standard deviation are nearly
equal

3.  r

4.  

quadform <- function(t,mu,Sigma) {
   (t-mu) %*% solve(Sigma) %*% (t-mu)
}

print(quadform(c(5,12,13),c(3,6,9),rbind(c(10,2,2),c(2,10,2),c(2,2,10))))
# 4.43

5.  T_r <= t if and only if N(t) >= r, so

F_{T_r}(t) = P[N(t) >= r] = 1 - P[N(t) < r] = 1 - F_N(t)(r-1)

F_Tr <- function(t,r,lambda){
   1 - ppois(r-1,lambda*t)
}

print(F_Tr(11,4,0.25))  # 0.29696