Introduction to Probability Distributions - Random Variables
A random variable is defined as a function that associates a real number (the probability value) to an outcome of an experiment.
In other words, a random variable is a generalization of the outcomes or events in a given sample space. This is possible since the random variable by definition can change so we can use the same...
Variance and Standard Deviation of a Random Variable
We have already looked at Variance and Standard deviation as measures of
dispersion under the section on
Averages. We can also measure the dispersion of Random variables across a given distribution using Variance and Standard deviation. This allows us to better understand whatever the distribution represents.
Expected Values of Random Variables
We already looked at finding the mean in the section on
averages. Random variables also have means but their means are not calculated by simply adding up the different variables.
The mean of a random variable is more commonly referred to as its Expected Value, i.e. the value you expect to obtain should you carry out some experiment whose outcomes...