QUESTION 1 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 tickmarks labeled: 0.5, 1, 1.5, 2, 2.5. The vertical axis is labeled: f(x), and has tickmarks 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 tickmark labeled 0.5 and to the right of the tickmark 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 tickmarks: 0.5, 1, 1.5, 2, 2.5. The vertical axis is labeled: f(x), and has tickmarks: 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 tickmark 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 tickmarks: 0.5, 1, 1.5, 2, 2.5. The vertical axis is labeled: f(x), and has tickmarks: 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 tickmark 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 tickmarks labeled: 0.5, 1, 1.5, 2, 2.5. The vertical axis is labeled: f(x), and has tickmarks 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 tickmark labeled 0.5 and to the right of the tickmark 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).

Answered: The random variable x is known to be…

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

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QUESTION 1

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 tickmarks labeled: 0.5, 1, 1.5, 2, 2.5. The vertical axis is labeled: f(x), and has tickmarks 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 tickmark labeled 0.5 and to the right of the tickmark 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 tickmarks: 0.5, 1, 1.5, 2, 2.5. The vertical axis is labeled: f(x), and has tickmarks: 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 tickmark labeled 1 on the vertical axis. This line segment connects the vertical line segment with the vertical axis.

A 2 unit long vertical line segment begins at 1 on the horizontal axis.
A 1 unit long horizontal line segment begins at the tickmark labeled 2 on the vertical axis. This line segment connects the vertical line segment with the vertical axis.

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 tickmark labeled 0.5 and to the right of the tickmark 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).

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