A random variable X has the probability density function of the attached graph (see attached photo):a) What is the expected value of X?b) Compute P(-500 < X < -250). The image displays a symmetrical triangular graph centered on the x-axis. The horizontal axis ranges from -500 to 500, and the vertex of the triangle is aligned with the y-axis at the point where x = 0. The highest point of the triangle, labeled as "h," represents the peak height.### Diagram Description:- **X-axis**: Labeled from -500 to 500.- **Y-axis**: Vertical line at x = 0 indicating symmetry.- **Triangle**: - The two sides of the triangle slope downwards from the peak at "h," meeting the x-axis at -500 and 500. - The height "h" is the maximum value reached by the triangle above the x-axis.

The total area under the probability density function =1 Area of the given graph is: Area of a…

Answered: -500 500

Math

Probability

-500 500

A First Course in Probability (10th Edition)

10th Edition

ISBN:9780134753119

Author:Sheldon Ross

Publisher:Sheldon Ross

Chapter1: Combinatorial Analysis

Section: Chapter Questions

Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...

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Concept explainers

Continuous Probability Distributions

Probability distributions are of two types, which are continuous probability distributions and discrete probability distributions. A continuous probability distribution contains an infinite number of values. For example, if time is infinite: you could count from 0 to a trillion seconds, billion seconds, so on indefinitely. A discrete probability distribution consists of only a countable set of possible values.

Normal Distribution

Suppose we had to design a bathroom weighing scale, how would we decide what should be the range of the weighing machine? Would we take the highest recorded human weight in history and use that as the upper limit for our weighing scale? This may not be a great idea as the sensitivity of the scale would get reduced if the range is too large. At the same time, if we keep the upper limit too low, it may not be usable for a large percentage of the population!

Question

A random variable X has the probability density function of the attached graph (see attached photo):

a) What is the expected value of X?

b) Compute P(-500 < X < -250).

The image displays a symmetrical triangular graph centered on the x-axis. The horizontal axis ranges from -500 to 500, and the vertex of the triangle is aligned with the y-axis at the point where x = 0. The highest point of the triangle, labeled as "h," represents the peak height.

### Diagram Description:
- **X-axis**: Labeled from -500 to 500.
- **Y-axis**: Vertical line at x = 0 indicating symmetry.
- **Triangle**:
- The two sides of the triangle slope downwards from the peak at "h," meeting the x-axis at -500 and 500.
- The height "h" is the maximum value reached by the triangle above the x-axis.

Expression, rule, or law that gives the relationship between an independent variable and dependent variable. Some important types of functions are injective function, surjective function, polynomial function, and inverse function.

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