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Chapter 8: Problem 7

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 a die is thrown until a 2 appears

Short Answer

Expert verified
The random variable \(X\) represents the number of times a die is thrown until a 2 appears. The minimum value of \(X\) is 1, and there is no maximum value as the die can be thrown indefinitely. The range of values for \(X\) is the set \(\{1, 2, 3, ...\}\). Therefore, \(X\) is an infinite discrete random variable.

Step by step solution

01

Identify the Random Variable

The random variable \(X\) represents the number of times a die is thrown until a 2 appears.
02

Determine the Minimum Value of \(X\)

The minimum value of \(X\) can be 1, which occurs if a 2 appears on the very first throw.
03

Determine if the Maximum Value of \(X\) is Finite or Infinite

There is no maximum value of \(X\) as the die can be thrown any number of times until a 2 appears. Theoretically, this could go on indefinitely. Therefore, the maximum value of \(X\) is infinite.
04

Describe the Range of Values for \(X\)

The range of values for the random variable \(X\) is any positive integer starting from 1, which can be written as the set \(\{1, 2, 3, ...\}\).
05

Classify the Random Variable

Since the random variable \(X\) is related to rolling a die and its range of values is infinite, we can classify \(X\) as an infinite discrete random variable.

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