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Chapter 8: Problem 9

Give the range of values that the random variable \(X\) may assume and classify the random variable as finite discrete, infinite discrete, or continuous. \(X=\) The distance in miles a commuter travels to work

Short Answer

Expert verified
The random variable $X$ has a range from 0 to 150 miles (\(X \in [0, 150]\)), and it is classified as a continuous random variable.

Step by step solution

01

Determine the range of values for the random variable X

The random variable X represents the distance (in miles) a commuter travels to work. From a practical point of view, the distance cannot be negative, so the lower limit is zero (0). There is no strict upper limit, but we could assume a reasonable maximum distance for a daily commute, for example 150 miles. Therefore, the range of values for X will be from 0 to 150 miles, including both endpoints. We can represent this range using the notation: \(X \in [0, 150]\).
02

Classify the random variable X

As the random variable X represents the distance a commuter travels to work, it can be assumed that the distances might have decimal values, and not restricted to only integers. Moreover, there are infinite possible decimal values in between two integers. So the random variable X is neither finite discrete nor infinite discrete. Since distances can assume any value in the continuous range from 0 to 150 miles, the random variable X is continuous. Final answer: The random variable X has a range from 0 to 150 miles, and it is classified as a continuous random variable.

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