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Chapter 6: Problem 2

Let \(x\) be a continuous random variable. What is the probability that \(x\) assumes a single value, such as \(a\) ?

Short Answer

Expert verified
The probability that a continuous random variable \(x\) can assume a single value \(a\) is 0.

Step by step solution

01

Understanding continuous random variables

A continuous random variable is a random variable where the data can take infinitely many and uncountable values. For example, the height of a person, time taken to perform a task, and distances are all continuous random variables.
02

Probability of a single value in a continuous distribution

In a continuous distribution, the probability of the variable assuming any specific exact value is always zero. This is because the set of potential values is infinite. Hence, any single point has no width and covers no proportion of the total possible outcomes.
03

Conclusion

Hence, the probability that a continuous random variable \(x\) will assume any specific single value \(a\) is 0.

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