The random variable x is known to be uniformly distributed between 0.5 and 1.0.
(a) Show the graph of the probability density function. The graph has a shaded area. The horizontal axis is labeled: x and has tick marks: 0.5, 1, 1.5, 2, 2.5. The vertical axis is labeled: f(x), and has tick marks: 1, 2, 3. The shaded area is the region bounded by the horizontal axis, the vertical axis, and the following line segments:
- A 2 unit long vertical line segment begins at 1 on the horizontal axis.
- A 1 unit long horizontal line segment begins at the tick mark labeled 2 on the vertical axis. This line segment connects the vertical line segment with the vertical axis.
The graph has a shaded area. The horizontal axis is labeled: x and has tick marks: 0.5, 1, 1.5, 2, 2.5. The vertical axis is labeled: f(x), and has tick marks: 1, 2, 3. The shaded area is the region bounded by the horizontal axis, the vertical axis, and the following line segments:
- A 1 unit long vertical line segment begins at 1 on the horizontal axis.
- A 1 unit long horizontal line segment begins at the tick mark labeled 1 on the vertical axis. This line segment connects the vertical line segment with the vertical axis.
The graph has a shaded area. The horizontal axis is labeled: x, and has tick marks labeled: 0.5, 1, 1.5, 2, 2.5. The vertical axis is labeled: f(x), and has tick marks labeled: 1, 2, 3. The shaded area is the region bounded by the horizontal axis and the following line segments:
- A 1 unit long vertical line segment begins at 0.5 on the horizontal axis.
- A 1 unit long vertical line segment begins at 1 on the horizontal axis.
- A 0.5 unit long horizontal line segment begins above the horizontal axis tick mark labeled 0.5 and to the right of the tick mark labeled 1 on the vertical axis. This line segment connects the two vertical line segments.
The graph has a shaded area. The horizontal axis is labeled: x, and has tick marks labeled: 0.5, 1, 1.5, 2, 2.5. The vertical axis is labeled: f(x), and has tick marks labeled: 1, 2, 3. The shaded area is the region bounded by the horizontal axis and the following line segments:
- A 2 unit long vertical line segment begins at 0.5 on the horizontal axis.
- A 2 unit long vertical line segment begins at 1 on the horizontal axis.
- A 0.5 unit long horizontal line segment begins above the horizontal axis tick mark labeled 0.5 and to the right of the tick mark labeled 2 on the vertical axis. This line segment connects the two vertical line segments.
(b) Compute P(x = 0.75).
(c) Compute P(0.5 ≤ x ≤ 0.75).
(d) Compute P(0.6 < x < 1.0).