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In: Statistics and Probability

STAT 150 The amount X, in GBs, of mobile data Sam uses in a given month...

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)?

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