Random Variables and Mathematical Expectation

Random Variables and Mathematical Expectation

Introduction

As an application of probability, there are two more concepts namely random variables and probability distributions. Before seeing the definition of probability distribution, random variable needs to be explained. It has been a general notion that if an experiment is repeated under identical conditions, values of the variable so obtained would be similar. However, there are situations where these observations vary even though the experiment is repeated under identical conditions. As the result, the outcomes of the variable are unpredictable and the experiments become random.

We have already learnt about random experiments and formation of sample spaces. In a random experiment, we are more interested in, x number associated with the outcomes in the sample space rather than the individual outcomes. These numbers vary with different outcomes of the experiment. Hence it is a variable. That is, this value is associated with the outcome of the random experiment. To deal with such situation we need a special type of variable called random variable.