The continuous random variable X takes values in the interval 0 ≤ x ≤ 5 only. For 0 ≤ x ≤ 5 the graph of its probability density function f consists of two straight line segments, as shown in the diagram.

a. Find k and show that f is given by

b. The random variable Y is given by Y = X².

i. Find the probability density function of Y.

ii. Show that E(Y) = 10.25.

iii. Show that the median of Y is the square of the median of X.

Transcribed Image Text:

x 0< x< 2 f(x) = 2くx<5 4 0 otherwise.