Binomial Random Variable
According to Kellar (2014) in his book Statistics for Management and Economics, he has mentioned that following conditions have to be satisfied for a variable to be binomial random variable:
There is fixed or known number of trials
Every trial can have exactly two possible outcomes; success or failure
Each and every trial in the experiment is independent of each other (Kellar, 2014, p. 241).
Example from my life
There can be many examples from my daily life which can fulfill the requirements of a binomial random variable. As a simple example, I can say “my daily attendance in the month of April 2016 if I drive from home to school every day”.
I exactly know the number of days for which school will be open in April 2016. Thus, the number of fixed trials is known and it can’t vary in normal circumstances. Thus, I say, the number of trials, n are 21. Now, as I drive every day to the school, there are only two outcomes. Either I will reach the school or for some reason, I will not. Thus, there are only two possible outcomes. One, I will reach the school and second, I will not. If the probability of reaching school is p, the probability of not reaching school will always be 1-p. Let’s now look at the last qualifier. If I do not reach the school on a specific day because I went somewhere else, the next day when I drive to school will be independent of this absence. Thus, every day, I can drive to school without depending on the previous or next attempts of driving to school. Thus, the probability for each attempt is independent with exactly the same probability of p for attending the school and 1-p for not attending.
There can be many more examples. Taking the final term exams is another example. There are two outcomes; pass or fail. No test is dependent on another and I exactly know how many tests I need to take.
References
Kellar, G (2014). Statistics for Management and Economics. Stamford, CT. Cengage Learning.
