The document presents the probability density function of a continuous random variable x as f(x) = 0.5x for the range 0 < x < 2. It states that the probability P(1 < x < 1.5) can take on one of the following values: 0.5625, 0.3125, 0.1250, or 0.4375.

1. If the probability density function of a continuous random variable X is f ( x ) = 0.5 x for 0 < x <
2 , then P ( 1 < X < 1.5 ) is 0.5625 0.3125 0.1250 0.4375