Problem

A social worker is involved in a study about fami…

02:24

Problem 5 Medium Difficulty

a. The variables in Exercise 5.3 are either discrete or continuous. Which are they and why?
b. Explain why the variable "number of dinner guests for Thanksgiving dinner" is discrete.
c. Explain why the variable "number of miles to your grandmother's house" is continuous.

Answer

a. discrete, count; continuous, measurable
b. count
c. measurable

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Intro Stats / AP Statistics

Elementary Statistics

Chapter 5

Probability Distributions

Section 1

Random Variables

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Video Transcript

this question gives us a couple of random variables and asks us to consider whether or not they're discrete or continuous part. A. The first part of this question asked us to consider our answers to questions. Five point question number three and question number three Accessed asked us to. Ah, answer. Take a survey of a number of siblings of our classmates and also the length of a conversation, the last conversation that we had with our mothers. Length of convo. Now we already looked at these random variables in depth a little bit in question three. But this asks us whether or not there, whether they're discreet or whether they continuous. So let's take a look. The 1st 1 the number of siblings, what we know right away that this is a count. We're counting the number of siblings and so automatically, when you're thinking counts, you should think of discrete. Anything that you can't have 1/2 of is automatically a discreet variable, discreet, random variable. Now, of course, there are. You can have half siblings, but that's not what we're talking about. In this instance we're talking about, um, the number of whole siblings that you have. So, no, you have 012 any whole number. But you can't have, like, 1/3 of a sibling. Um, And then when we talk about the length of the last conversation we had with our mothers again, things like time when you're talking about, like, length of time or, uh, number, number of days. Things like this, Um, time most of the time, be a continuous random variables. That's because there are uncountable number of values that this random variable could take. Say, for instance, uh, you could measure very, very accurately to the nanosecond How long you have so many possible outcomes for this A length of conversation. Um, and it is more specific your measurements get the more ah, uh, more options. You have more number outcomes you have for this random variable. Next we have, um it asked us about the number of guests at a Thanksgiving dinner again. Here were counting. Whenever you think whenever you're counting something, you can't have half of a guest. Even if people leave early, they're still like a guest. So whenever we're counting something, we know automatically, it's discreet And part c finally asked us. Thea number of miles to get to Grandma's house. Now the number of miles, um is it looks like account. You can you see again? Number of miles were counting miles, but consider this, um, we can have half of a mile, so I can say it's 2.5 miles to Grandma's house, and that makes sense that makes, ah, that's a valid outcome of this random variable. Um, so there's really are unaccountably infinite number of outcomes that this variable could take. Um, it's a spectrum. You can go anywhere from anywhere between zero and inf. Well, not an infinite number of miles again. We have physical limitations, but still uncounted Lee infinite number of outcomes for the number of miles to grandma's house. Therefore, this is a continuous random variable.

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