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Chapter 8: Problem 3

A die is rolled repeatedly until a 6 falls uppermost. Let the random variable \(X\) denote the number of times the die is rolled. What are the values that \(X\) may assume?

Short Answer

Expert verified
The random variable \(X\) may assume any positive integer value, as it represents the number of times a die is rolled until a 6 appears (\(X = 1, 2, 3, 4, ... \)). There is no upper limit to the number of times a die can be rolled until a 6 appears.

Step by step solution

01

Identify the possible outcomes of rolling a die

There are a total of 6 sides on a die with numbers ranging from 1 to 6. So, there are 6 possible outcomes when rolling the die, with each outcome having a probability of \(\frac{1}{6}\).
02

Determine the possible values of X

Since X is the number of times a die is rolled until a 6 appears, the possible values of X can be any natural number, i.e., 1, 2, 3, 4, 5, and so on. There is no upper limit to the number of times a die can be rolled until a 6 appears. To summarize, the values that the random variable \(X\) may assume are all positive integers (\(X = 1, 2, 3, 4, ... \)).

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