Math Is Fun Forum

genericname

Member

Registered: 2012-05-16

Posts: 52

Random variable question

Hi, I am a bit confused about this problem.

For each of the following random variables, tell whether it would naturally represent a finite, discrete or continuous random variable. Explain your reasoning.

a) X is the number of customers who walk into a shop between noon and 1PM on some particular day.
b) X is the amount of orange juice in a randomly chosen 8-ounce carton of juice.
c) X is the amount of times you play the lottery until you win? We'll assume that once you win you stop playing.
d) X is the number of women in a randomly chosen sample of 500 New York City residents.

For the answers I got:

a) Finite because the amount of people between the noon and 1PM are countable.
b) Continuous because the amount of juice is uncountable.
c) Continuous because you don't know when you will win.
d) Discrete because it is taking a number of people from a set amount.

Bob

Administrator

Registered: 2010-06-20

Posts: 10,626

Re: Random variable question

hi genericname

In all the maths courses I've come across data sets have only been divided into discrete and continuous.

There's a simple definition / example at

http://www.mathwords.com/d/discrete.htm

So how has 'finite' defined in this context.

Bob

---

Children are not defined by school ...........The Fonz
You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei
Sometimes I deliberately make mistakes, just to test you!  …………….Bob

genericname

Member

Registered: 2012-05-16

Posts: 52

Re: Random variable question

I think it means that something can be completely counted. Not quite sure.

Bob

Administrator

Registered: 2010-06-20

Posts: 10,626

Re: Random variable question

Oh.

That's two of us who don't know then.

a) X is the number of customers who walk into a shop between noon and 1PM on some particular day.
b) X is the amount of orange juice in a randomly chosen 8-ounce carton of juice.
c) X is the amount of times you play the lottery until you win? We'll assume that once you win you stop playing.
d) X is the number of women in a randomly chosen sample of 500 New York City residents.

I'd say (b) is definitely continuous.

The others are all positive integers so that would make them discrete.  I cannot see any speicial quality that would make some 'finite'.  They are all countable but all discrete data has to be that or you don't 'know' it.

Sorry I cannot be more help. 

What is the course?

Bob

---

Children are not defined by school ...........The Fonz
You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei
Sometimes I deliberately make mistakes, just to test you!  …………….Bob

genericname

Member

Registered: 2012-05-16

Posts: 52

Re: Random variable question

The course is Elementary Probability and Statistics.

Bob

Administrator

Registered: 2010-06-20

Posts: 10,626

Re: Random variable question

I've had a search on-line and can only find two categorisations of data: discrete and continuous.

See:

http://www.chegg.com/homework-help/defi … tinuous-31

However the Wiki article does allow that discrete distributions may be finite or infinite (by which they mean no upper limit but can be counted)

See:

http://en.wikipedia.org/wiki/Probability_distribution

About one third of the way down the article look for the section:   "Discrete probability Distribution"

So here's my best shot at the answers:

a) X is the number of customers who walk into a shop between noon and 1PM on some particular day.  discrete and unbounded"
b) X is the amount of orange juice in a randomly chosen 8-ounce carton of juice.  continuous
c) X is the amount of times you play the lottery until you win? We'll assume that once you win you stop playing. discrete and unbounded
d) X is the number of women in a randomly chosen sample of 500 New York City residents. discrete and finite

Bob

---

Children are not defined by school ...........The Fonz
You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei
Sometimes I deliberately make mistakes, just to test you!  …………….Bob