You may make reference to the following three results in this question:
$\sum_{i=m}^n c = (n-m+1) c$
$\sum_{i=1}^n i = \frac{1}{2} n(n+1)$
$\sum_{i=1}^n i^2 = \frac{1}{6} n(n+1)(2n+1).$

The random variable $X$ has the discrete Uniform distribution given by
$P(X = j) = k$ for $j = 2, 3, 4, ..., 29$. Find (to 3 d.p.):

Part a)
The value of $k$ given as a fraction.


Part b)
The expectation of $X$ given to three decimal places.

Part c)
The variance of $X$ given to three decimal places.