The random variable x is known to be uniformly distributed between 10 and 20.(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: 10, 20, 30, 40, 50. The vertical axis is labeled: f(x), and has tickmarks labeled: 0.05, 0.1, 0.15, 0.2. The shaded area is the region bounded by the horizontal axis and the following line segments.A 0.1 unit long vertical line segment begins at 30 on the horizontal axis.A 0.1 unit long vertical line segment begins at 40 on the horizontal axis.A 10 unit long horizontal line segment begins above the horizontal axis tickmark labeled 30 and to the right of the tickmark labeled 0.1 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 labeled: 10, 20, 30, 40, 50. The vertical axis is labeled: f(x), and has tickmarks labeled: 0.05, 0.1, 0.15, 0.2. The shaded area is the region bounded by the horizontal axis and the following line segments.A 0.05 unit long vertical line segment begins at 30 on the horizontal axis.A 0.05 unit long vertical line segment begins at 40 on the horizontal axis.A 10 unit long horizontal line segment begins above the horizontal axis tickmark labeled 30 and to the right of the tickmark labeled 0.05 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 labeled: 10, 20, 30, 40, 50. The vertical axis is labeled: f(x), and has tickmarks labeled: 0.05, 0.1, 0.15, 0.2. The shaded area is the region bounded by the horizontal axis and the following line segments.A 0.05 unit long vertical line segment begins at 10 on the horizontal axis.A 0.05 unit long vertical line segment begins at 20 on the horizontal axis.A 10 unit long horizontal line segment begins above the horizontal axis tickmark labeled 10 and to the right of the tickmark labeled 0.05 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 labeled: 10, 20, 30, 40, 50. The vertical axis is labeled: f(x), and has tickmarks labeled: 0.05, 0.1, 0.15, 0.2. The shaded area is the region bounded by the horizontal axis and the following line segments.A 0.1 unit long vertical line segment begins at 10 on the horizontal axis.A 0.1 unit long vertical line segment begins at 20 on the horizontal axis.A 10 unit long horizontal line segment begins above the horizontal axis tickmark labeled 10 and to the right of the tickmark labeled 0.1 on the vertical axis. This line segment connects the two vertical line segments.(b)Compute P(x < 15). (c)Compute P(12 ≤ x ≤ 14). (d)Compute E(x). (e)Compute Var(x). (Round your answer to two decimal places.)

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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The random variable x is known to be uniformly distributed between 10 and 20.

(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: 10, 20, 30, 40, 50. The vertical axis is labeled: f(x), and has tickmarks labeled: 0.05, 0.1, 0.15, 0.2. The shaded area is the region bounded by the horizontal axis and the following line segments.

A 0.1 unit long vertical line segment begins at 30 on the horizontal axis.
A 0.1 unit long vertical line segment begins at 40 on the horizontal axis.
A 10 unit long horizontal line segment begins above the horizontal axis tickmark labeled 30 and to the right of the tickmark labeled 0.1 on the vertical axis. This line segment connects the two vertical line segments.

A 0.05 unit long vertical line segment begins at 30 on the horizontal axis.
A 0.05 unit long vertical line segment begins at 40 on the horizontal axis.
A 10 unit long horizontal line segment begins above the horizontal axis tickmark labeled 30 and to the right of the tickmark labeled 0.05 on the vertical axis. This line segment connects the two vertical line segments.

A 0.05 unit long vertical line segment begins at 10 on the horizontal axis.
A 0.05 unit long vertical line segment begins at 20 on the horizontal axis.
A 10 unit long horizontal line segment begins above the horizontal axis tickmark labeled 10 and to the right of the tickmark labeled 0.05 on the vertical axis. This line segment connects the two vertical line segments.

A 0.1 unit long vertical line segment begins at 10 on the horizontal axis.
A 0.1 unit long vertical line segment begins at 20 on the horizontal axis.
A 10 unit long horizontal line segment begins above the horizontal axis tickmark labeled 10 and to the right of the tickmark labeled 0.1 on the vertical axis. This line segment connects the two vertical line segments.

(b)

Compute

P(x < 15).

(c)

Compute

P(12 ≤ x ≤ 14).

(d)

Compute

E(x).

(e)

Compute

Var(x).

(Round your answer to two decimal places.)

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