Question

Product codes of 2, 3, 4, 5, or 6 letters are equally likely. What is the mean and variance of the number of letters in the codes

Answer 1

Answer:

$Mean = 4$

$Var = \frac{25}{12}$

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,

$Mean = \frac{a+b}{2}$

Where

$a = Lower\ Bound = 2$

$b = Upper\ Bound = 6$

$Mean = \frac{a+b}{2}$

$Mean = \frac{2 + 6}{2}$

$Mean = \frac{8}{2}$

$Mean = 4$

Variance of a uniform distribution is calculated as thus;

$Var = \frac{(b-a+1)^2}{12}$

Substitute values for a and b

$Var = \frac{(6-2+1)^2}{12}$

$Var = \frac{5^2}{12}$

$Var = \frac{25}{12}$