What are the continuous and discrete random variables involved in rolling a die 20 times?

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goreadabook | High School Teacher | (Level 2) Assistant Educator

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To begin with, a random variable is a variable whose value occurs by chance.  In other words, it doesn't have a single fixed value.  When you roll a die, the number that you roll is a random variable because it occurred by chance.  More specifically, a continuous random variable is a variable whose value is any number within a given range.  For example, if you wanted to know how many 3's you rolled in 20 turns, the answer would be a continuous random variable.  This is because the value would be somewhere within the range of 0-20.  Finally, a discrete random variable is a variable whose value can only take on a specific, countable number.  Unlike continuous variables, there are no in-between values.  The given value of any die roll is an example of a discrete random variable.  It is a specific, countable number that occurred by chance.