A weather channel has the local forecast on the hour and at 10, 25, 30, 45, and 55 minutes past.

Suppose that you wake up in the middle of the night and turn on the TV and let X be the time

you have to wait to see the local forecast, measured in hours.

Find the density function of X.

My thoughts are to break up the hour into the following intervals:

0, (0, 10), 10, (10, 25), 25, (25, 30), 30, (30, 45), 45, (45, 55), 55, (55, 60)

The largest interval is 15 minutes, so the wait time can range from 0 to 15 minutes.

Not sure how to proceed from here on. Can someone help?