A discrete random variable can only take particular values. They are numbers that are countable and are described by a probability distribution. They can be represented by a table, a graph or a formula which takes into account of the probability p(x) for every value of x.
Now let’s look at probability functions. There are 3 rules that we need to remember when we are doing a probability functions question.
for all of x
The three main measures of centre are mean, median and mode.
The mean is also known as the expected value is used to calculate the average value we would expect to occur from the function in the long term and is calculated with the formula:
Median is the middle value of the distribution in which 50% of the distribution is larger than it and 50% is less than it.
The mode is the discrete value which is most commonly occurring discrete value.
Question 7 from the 2013 VCAA exam 1
As the sum of all values of p(x) must equal to 1, in order to solve for p, we need to add all the values of Pr(X=x) together and make them equal to one.
This question is related to the previous question that we have gone through. First, we need to substitute this p value into the table.
In order to find the expected value. We need to find the sum of all the values of x times by the probability that it takes, as the formula for the mean above shows us.
The mode for this set is 3 as that is the value most likely to occur.
Looking again at the original table we can see that 46.7% of the time the value of the number will be less than two, but the probability that is less or equal to two is 56.7%. This means that 2 sits on the range of 50% of the distribution is larger than it and 50% is smaller. Therefore it is the median value.
Want to suggest an edit? Have some questions? General comments? Let us know how we can make this resource more useful to you.