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Chapter 8: Problem 11

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 number of times an accountant takes the CPA examination before passing

Short Answer

Expert verified
The range of values that the random variable \(X\) may assume is \(X = \{1, 2, 3, ... \}\), which includes all positive integers. Since the range is composed of whole numbers and infinite in length, the random variable \(X\) is classified as an infinite discrete random variable.

Step by step solution

01

Determine the minimum number of attempts

The minimum number of attempts the accountant would need to take the CPA examination before passing is 1, since they could pass it on their first try.
02

Determine if there's a maximum number of attempts

There is no maximum number of attempts for taking the CPA examination before passing, as the accountant can theoretically keep taking the exam until they pass.
03

Find the range of values for \(X\)

Based on Steps 1 and 2, the range of values for \(X\) includes all whole number attempts starting from 1, and it has no upper bound. In other words, the range is \(X = \{1, 2, 3, ... \}\), which represents all positive integers.
04

Classify the random variable

Since the random variable \(X\) represents the number of times an accountant takes the CPA examination before passing, it can take any whole number value within the range we found in Step 3. The range is composed of whole numbers (discrete) and infinite in length as it has no upper bound. Thus, the random variable \(X\) is classified as an infinite discrete random variable.

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