Last year, Pinwheel Industries introduced a new toy. It cost $
8
,
500
$
8
,
500
to develop the toy and $
30
30
to manufacture each toy. Fill in the blanks below as appropriate.

The random variable x has probability density function f (x) = k(−x²+5x−4) 1 ≤ x ≤ 4 or =0 1 show that k = 2/9 find 2 e(x), 3 the mode of x, 4 the cumulative distribution function f(x) for all x. 5 evaluate p(x ≤ 2.5). 6 deduce the value of the median and comment on the shape of the distribution.