1.  committee problem, Sec. 3.9.3, specifically the variables G_i

2.  1/sigma^2

3.  (iv), (v)

4.  (iv)

5.  

F_X <- function(t){
  f_x <- function(x) 1/(1+x^2)
  cc <- 1/ integrate(f_x,-5,5)$value
  cc * integrate(f_x,-5,t)$value
}

print(F_X(1))  # 0.79