A random variable is called discrete if it can assume finite number of values. If two bulbs are selected from a certain lot, the number of defective bulbs may be 0, 1 or 2. The range of the variable is from 0 to 2 and random variable can take some selected values in this range. The number of defective bulbs cannot be 1.1 or or 3 etc. This random variable can take only the specific values which are 0, 1 and 2. When two dice are rolled the total on the two dice will be 2, 3, …, 12. The total on the two dice is a discrete random variable.
Discrete Probability Distribution:
The probability of some interval can be calculated by adding the probabilities of all points in the interval. For example.
(i) for (ii) for Example: A digit is selected from the first 8 natural numbers. Write the probability distribution of where is the number of factors (divisors) of digits. Solution: It is assumed here that the probability of selection for each digit is . We can write:
The information in the above table can be summarized as below in the form of table of probability distribution.
The probability of is 4/8 which has been obtained by adding 1/8 four times. Similarly the probability of 4 is 2/8 which has been obtained by adding 1/8 two times.
Example:
Solution:
Here It is assumed here that the two bulbs are selected independently because there is very large number of bulbs in the factory. According to multiplication law of independent events, we have
The possible outcomes, the random variable and the corresponding probabilities are put in the following tables:
The above information can be collected as below in the form of a probability distribution of the random variable.
