It may assume any numerical value in an interval or collection of intervals1 pointcontinuous random variablediscrete random variablerandom variable
Question
It may assume any numerical value in an interval or collection of intervals
- point
- continuous random variable
- discrete random variable
- random variable
Solution
In your question, you're referring to different types of random variables in the context of probability and statistics. Here's a detailed explanation:
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Continuous Random Variable: This type can assume any numerical value within a given interval or collection of intervals. For instance, the height of individuals or the time taken to complete a task are examples of continuous random variables. They can take an infinite number of values.
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Discrete Random Variable: Unlike continuous random variables, discrete random variables can assume only specific numerical values, often integers. A typical example would be the number of students in a classroom or the result of rolling a die, where only certain outcomes (1 through 6) are possible.
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Random Variable: This is a broader term that encompasses both continuous and discrete types. A random variable is a function that maps outcomes of a random process to numerical values, allowing for probabilistic reasoning.
To summarize, when looking for a random variable that can take any numerical value within an interval, you are referencing a continuous random variable. Conversely, if only specific values can be attained, then you're discussing a discrete random variable.
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