**Probability Density Function**The probability density of a random variable $ X $ is given in the figure below.**Graph/Diagram Description:**A rectangular graph (bar) is shown over a horizontal axis. The base of the rectangle extends from $ x = 0 $ to $ x = 2 $, and its height is constant. The height of the rectangle represents the probability density. Points are marked at $ x = 0 $, $ x = 1 $, and $ x = 2 $ along the horizontal axis.Horizontal Axis Label: $ x $---From this density, the probability that $ X $ is between 0.4 and 1.02 is:\[ \text{Answer Box} \]By integrating the probability density function between the limits 0.4 and 1.02, we can determine the probability.

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Answered: The probability density of a random…

The probability density of a random variable X is given in the figure below. 1. From this density, the probability that X is between 0.4 and 1.02 is:

Calculus: Early Transcendentals

8th Edition

ISBN:9781285741550

Author:James Stewart

Publisher:James Stewart

Chapter1: Functions And Models

Section: Chapter Questions

Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...

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Question

**Probability Density Function**

The probability density of a random variable $ X $ is given in the figure below.

**Graph/Diagram Description:**
A rectangular graph (bar) is shown over a horizontal axis. The base of the rectangle extends from $ x = 0 $ to $ x = 2 $, and its height is constant. The height of the rectangle represents the probability density. Points are marked at $ x = 0 $, $ x = 1 $, and $ x = 2 $ along the horizontal axis.

Horizontal Axis Label: $ x $

---

From this density, the probability that $ X $ is between 0.4 and 1.02 is:

\[ \text{Answer Box} \]

By integrating the probability density function between the limits 0.4 and 1.02, we can determine the probability.

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