Answer:
[tex]E(x) = 1.5\\[/tex]
Step-by-step explanation:
Given
[tex]n = 9[/tex] -- number of rolls
Required
The mean of 2's
The distribution follows binomial distribution where:
[tex]X \to Binomial(n,p)[/tex]
In this case:
[tex]p= \frac{1}{6}[/tex] ---- the theoretical probability of rolling 2
So, the mean of 2's is calculated using:
[tex]E(x) = np[/tex]
[tex]E(x) = 9 * \frac{1}{6}[/tex]
[tex]E(x) = \frac{9}{6}[/tex]
Simplify
[tex]E(x) = \frac{3}{2}[/tex] or
[tex]E(x) = 1.5\\[/tex]
