Answer: Option A
[tex]\sigma ^ 2 = 2.25[/tex]
Step-by-step explanation:
The number of faces obtained by flipping the coin 9 times is a discrete random variable.
If we call this variable x, then, the probability of obtaining a face in each test is p.
Where [tex]p = 0.5[/tex]
If we call n the number of trials then:
[tex]n = 9[/tex]
The distribution of this variable is binomial with parameters
[tex]p = 0.5\\\\n = 9[/tex]
For a binomial distribution, the variance "[tex]\sigma^2[/tex]" is defined as
[tex]\sigma ^ 2 = np(1-p)[/tex]
[tex]\sigma ^ 2 = 9(0.5)(1-0.5)[/tex]
[tex]\sigma ^ 2 = 9(0.5)(0.5)[/tex]
[tex]\sigma ^ 2 = 2.25[/tex]
