Answer:
[tex]Mean = 4[/tex]
[tex]Var = \frac{25}{12}[/tex]
Step-by-step explanation:
Given
Codes: 2,3,4,5,6
Required
Determine the Mean and Variance
Equally likely implies that the data follows a uniform distribution.
So,
[tex]Mean = \frac{a+b}{2}[/tex]
Where
[tex]a = Lower\ Bound = 2[/tex]
[tex]b = Upper\ Bound = 6[/tex]
[tex]Mean = \frac{a+b}{2}[/tex]
[tex]Mean = \frac{2 + 6}{2}[/tex]
[tex]Mean = \frac{8}{2}[/tex]
[tex]Mean = 4[/tex]
Variance of a uniform distribution is calculated as thus;
[tex]Var = \frac{(b-a+1)^2}{12}[/tex]
Substitute values for a and b
[tex]Var = \frac{(6-2+1)^2}{12}[/tex]
[tex]Var = \frac{5^2}{12}[/tex]
[tex]Var = \frac{25}{12}[/tex]
