7. Mrs. Garcia is conducting an experiment in which students in her physics class drop eggs from the second story of the high school. She wants to know what the speed of each egg will be before the egg hits the ground. The acceleration due to gravity is 9.8 m/s?

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.