Let X denote the number of hours you study during a randomly selected school day. The probability that X can take the values x, has the following form, where k is some unknown constant.
`P(X=x)={{:(0.1, "if "x =0),(kx, "if "x = 1 or 2 ),(k(5-x), "if " x=3 or 4),(0,"otherwise"):}`
(a) Find the value of k.
(b) What is the probability that you study at least two hours ? Exactly two hours? At most two hours?

Answer

(a) k=0.15, (b) 0.55