Identifying Discrete and Continuous Random Variables. In Exerc...

Question

Identifying Discrete and Continuous Random Variables. In Exercises 5 and 6, refer to the given values, then identify which of the following is most appropriate: discrete random variable, continuous random variable, or not a random variable.

a. IQ scores of statistics students

b. Exact heights of statistics students

c. Shoe sizes (such as 8 or 8½) of statistics students

d. Majors (such as history) of statistics students

e. The number of rolls of a die required for a statistics student to get the number 4

Accepted Answer

All right, hello, everyone. So this question says, each of the following scenarios can be described as a discrete random variable, a continuous random variable, or not a random variable. Which scenarios are continuous random variables? And here we have 5 different scenarios that we'll go over in detail later on. But for now, what does it actually mean? For something to be a discrete or continuous random variable or not a random variable at all. So first and foremost, it's important to recognize that random variables must result from a random process. Now, the difference is that a discrete random variable. Is countable Though it can take or it can be in a finite or an infinite sequence. A continuous random variable on the other hand. Can take any value. Within a given range, and again that range can be finite or infinite. Now, you would describe something as being or as not being a random variable when the data itself does not vary, or if it does not result from a random process. So before we get into the examples, I just want to point out that a discrete random variable. Can only be a whole number. Because it is countable. So now let's go to the first example here. Which says the number of pages in various novels in a library. So here, if you're counting the number of pages in a novel, again, you're counting, right, which means that you can only have whole numbers, making scenario A a discrete random variable, or a DRV as I'm writing here. Scenario B says the amount of milk in liters a cow produces in a day. Now, the amount of milk in this context is being measured, right? Because you're measuring the number of liters that are produced. Therefore, this value can Very continuously within a range, considering that the number of liters could be a decimal. It doesn't have to be a whole number. So therefore, scenario B is a continuous random variable or a CRV. Scenario C is the number of languages spoken by university professors. Now, the number of languages in this case is countable, which makes this a DRV. Now, scenario D says the types of plants in a botanical garden. Now, in this case, the types of plants refers to categories. And The types of plants in a botanical garden don't represent numerical values. Rather, you're grouping them based on what type of plant they are. Therefore, This would be not a random variable or NRV as I'm writing here. And then we have scenario E, which says the time in minutes it takes for a student to complete a math quiz. Now notice the keyword here, right? You're measuring the time that it took the student to complete the quiz in minutes, so you're measuring, which means that it can vary continuously and it could be a decimal. Making this a continuous random variable. So now, out of the 4 scenarios given, only 2 represent continuous random variables. Which brings us to our final answer of B and E. And there you have it. So with that being said, thank you so very much for watching, and I hope you found this helpful.

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Key Concepts

Discrete Random Variables

Continuous Random Variables

Random Variables

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