Understanding Random Variables
Hi, I'm Dr Nic,
and I'm going to help you learn what random variables are
and what they do.
I want to also explain discrete and continuous random variables.
In simple terms, a random variable is the result of a chance event
that you can measure or count.
For example, in our probability videos,
we looked at the probability of getting a lunch
with an apple and a banana cake.
This was the result of a chance event,
but it was not a random variable as it was not a number.
We will use the following example to learn about things
that ARE random variables.
Luke has an ice cream stand,
and sells hand-scooped, home-made ice creams in cones.
Luke wishes to analyse his sales,
and make decisions about employing an assistant,
and expanding his business.
Luke has collected data from the last month,
and can tell you how many ice creams were bought in each transaction.
The table lists the number of ice creams bought,
and the number of customers who bought that number of ice creams.
We can define
X
It is called
and is the result of a chance happening.
We estimate the probability for each value of
by finding the relevant frequencies from the historic or experimental data.
The distribution for
the number of ice creams one customer buys, looks like this.
As a dot diagram, it looks like this,
which could be rearranged to look like this.
We often like to show distributions as a graph.
We can use this distribution to answer questions.
Luke wants to know, what is the probability
that the next customer will buy exactly one ice cream?
We look on the table and tell him
that the probability that
Luke then asks,
'Out of 200 customers,
how many would we expect to buy more than three ice creams?'
We want to find the probability that
so we add up all the probabilities that apply.
The probability that
equals the probability that
plus the probability that
which equals .04 plus .04 plus .02,
which equals .1, or 10%.
.1 times 200 equals 20,
so we would expect 20 customers out of the next 200
to buy more than three ice creams.
This example of number of ice creams is an example of a discrete distribution
as you can only get whole numbers of ice creams.
Other things that can be modelled as discrete random variables are:
Number of customers who arrived in the next hour.
Number of customers who pay by cash.
Number of days in a month in which the stall is closed due to rain.
Number of cones that break while being filled.
The following can
because they cannot be counted:
The flavour topping a customer chooses.
The ethnicity of the customer.
The method the customer uses to pay.
Some random variables are continuous,
which means that they can take any value within a range, including fractions.
If we wish to model the weight of an ice cream,
it would take a range of values in grams,
so it would be modelled by a continuous random variable.
Luke is interested in how long he takes to serve a customer,
and how long to scoop an ice cream.
These would both be continuous random variables
measured in minutes or seconds.
For each of the following,
decide whether they would be modelled as a discrete random variable,
a continuous random variable,
or
Weight of a suitcase.
Number of emergency calls in an hour.
Marital status.
Time taken to get to a fire.
Length of a tulip stem.
Colour of a tulip flower.
Number of bulbs that produce flowers.
You can see the answers at the end of the video.
In later videos, we show how to find summary values of random variables,
and perform operations with them.
We also teach how to answer questions involving random variables,
and introduce specific distributions.
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Here are the answers.