According to a study I just made up, the probability a randomly selected individual will not cover their mouth when sneezing is 20 %. Suppose you sit in public and record the sneezing habits of 10 randomly selected people. i) Define the random variable associated with the experiment of recording the sneezing habits of 10 randomly selected people by giving both its definition and its probability mass function. ii) What is the probability that among 10 randomly selected people exactly 4 do not cover their mouth when sneezing? iii) What is the probability that among 10 randomly selected people fewer than 3 do not cover their mouths? iv) What is the expected value of 10 randomly selected people not covering their mouths when sneezing? v) What is the variance of 10 randomly selected people not covering their mouths when sneezing? vi) Suppose you now observe 15 randomly selected people rather than 10-what is the probability then that at most 2 do not cover their mouths when sneezing? vii) What is the probability that you observe at least 3 people not covering their mouths when sneezing if you are observing 15 random individuals?

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Contingency Table

A contingency table can be defined as the visual representation of the relationship between two or more categorical variables that can be evaluated and registered. It is a categorical version of the scatterplot, which is used to investigate the linear relationship between two variables. A contingency table is indeed a type of frequency distribution table that displays two variables at the same time.

Binomial Distribution

Binomial is an algebraic expression of the sum or the difference of two terms. Before knowing about binomial distribution, we must know about the binomial theorem.