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).

QUESTION 1: (a) The random variable x is known to be uniformly distributed between 0.5 and 1.0. That is, a=0.5,b=1.0. The uniform distribution is, fx=1b-a x∈a,b Substituting the value of parameters in the distribution gives the value of uniform distribution as: fx=11-0.5=10.5=2 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. The graph is,(b) The probability that x is equal to 0.75 is, Px=0.75=0 Thus, the probability that x is equal to 0.75 is 0. (c) The probability that x ranges from 0.5 to 0.75 is, P0.5≤x≤0.75=∫0.50.75fxdx=∫0.50.752dx=2x0.50.75=20.75-0.5=2×0.25=0.50 Thus, the probability that x ranges from 0.5 to 0.75 is 0.50. (d) The probability that x ranges from 0.6 to 1 is, P0.6<x<1=∫0.61fxdx=∫0.612dx=2x0.61=21-0.6=2×0.4=0.80 Thus, the probability that x ranges from 0.6 to 1 is 0.80.

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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