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,",",x=0),(kx,",","x=1 or 2"),(k(5-x),",","X=3 or 4 "),(0,",","otherwise"):}`
i. Find the value of k
ii. What is the probability that you study atleast two hours? Exactly 2 hours? Atmost 2 hours?

Answer

(a) k=0.15, (b) 0.55