In the previous post we covered covariance and correlation. In this post we will look at discrete and continuous random variables.
A probability distribution is a graphical presentation of the probabilities of all possible outcomes of a random variable X. The probabilities of all possible outcomes should sum to 1. Eg. For a toss of a coin there are two possible outcomes heads or tails. Therefore the probabilities of each of them are ½ and the sum of the probabilities is 1.
Discrete Random Variable
A discrete random variable is that for which the the number of all possible outcomes is a finite number. Eg. Toss of a coin. No. Of all possible outcomes is 2. Another example is the no. Of days it will rain in the month. The maximum possible outcomes is the no. Of days in the month and therefore it is a finite number.
Continuous Random Variable
For a discrete random variable p(x) = 0 if x cannotoccur. Eg. The possibility of it raining for 32 days in the month of January cannot occur as January has only 31 days. However for a continuous random variable p(x) can be 0 even if x canoccur. That is because from the infinite number of possibilities the possibility of one particular value occurring is so small that it is zero. However if you state a range of possibilities between which the values can lie then it can have a positive value. Eg: The possibility of getting 2 inches of rainfall from an infinite number of possibilities is very small. However the possibility of the rainfall being between 1.999999 and 2.0000001 inches has some positive value.