1.  innocent until proven guilty

2.  (ii), (vi)

3.  Setting the integral across the entire support equal to 1, we find
that 1 = c (1/3)(6^3 - 2^3), so c = 3/208.  Then F_x(s) is equal to the
integral of (3/208) t^2 from 2 to s, i.e. (1/208)(s^3 - 8).

cdf <- function(t) 
{
   (1/208) * (t^3 - 8)
}

print(cdf(3.5))  # 0.1676683

4.  

library(mlbench)
data(PimaIndiansDiabetes2)
age <- PimaIndiansDiabetes2$age
xbar <- mean(age)
s2 <- var(age)
tail <- -qnorm(0.01/2)
rad <- tail * sqrt(s2 / length(age))
print(c(xbar-rad,xbar+rad))  # (32.15,34.33)