1.  histogram

2.  1/sigma^2

3.  (i)

4.  

nt0 <- function(t)  # t can be any pos. number
{
   # N(t) = 0 if and only if X_1 > t
   # P(X_1 > t) = 1-t, either by integrating or just noting
   #    that P(X in (a,b)) = b-a due to "all points being 
   #    equally likely"
   if (t < 1) return(1-t)
   return(1)
}

print(nt0(0.6))  # 0.4
print(nt0(1.6))  # 0


5.

haz <- function(t)
{
   # F_X(t) = t^2
   2*t / (1 - t^2)
}

print(haz(0.5))  # 1.33