The probability distribution often deals with variables as a ‘quantity that may assume any one of a set of values’. In probability distribution we deal with random variables - variables whose observed value is determined by chance.
The random variable in probability distribution that represent outcomes of an experiment if these outcomes are numerical or if real numbers can be assigned to them.
Types of Random variables:
1. Discrete Random variable
2. Continuous Random variable.
If a Discrete random variable in probability distribution takes only a finite or a countable number of values, it is called a discrete random variable.
1. The number of heads obtained when two coins are tossed is a discrete random variable as X assumes the values 0, 1 or 2 which form a countable set.
2. Number of Aces when ten cards are drawn from a well shuffled pack of 52 cards.
The random variable X assumes 0, 1, 2, 3 or 4 which is again a countable set.
i.e., X (No aces) = 0, X (one ace) = 1, X (two aces) = 2,
X (three aces) = 3, X (four aces) = 4
A Continuous Random Variable in probabiltiy distribution X is said to be continuous if it can take all possible values between certain given limits. i.e., X is said to be continuous if its values cannot be put in 1 − 1 correspondence with N, the set of Natural numbers.
1. The life length in hours of a certain light bulb.
2. Let X denote the ph value of any chemical compound which is randomly selected between 0 and 14 is possible.
3. If in the study of ecology of a lake, X = the depth at such location is a continuous random variable. The limit will be between the maximum and minimum depth in the region sampled.