In: Statistics and Probability
STAT 150 The amount X, in GBs, of mobile data Sam uses in a given month is uniformly distributed between 0 and 10. The mobile data plan Sam is subscribed to charges Y dollars per months, where
Y = 20 X < 3,
=10 [X], 3 ≤ X < 6,
=10X X ≥ 6.
where [X] denotes the floor of x.
(1) What is the probability P (Y < 45)?
(2) What is the E(Y)?