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

Question

asked Sep 23, 2021 230k views

1 Answer

Ravinda Lakshan · Answer 1 · 2021-09-27T10:01:24+0000

Answer:

Mean = 4

Var = (25)/(12)

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 = (a+b)/(2)

Where

$a = Lower\ Bound = 2$

$b = Upper\ Bound = 6$

Mean = (a+b)/(2)

Mean = (2 + 6)/(2)

Mean = (8)/(2)

Mean = 4

Variance of a uniform distribution is calculated as thus;

Var = ((b-a+1)^2)/(12)

Substitute values for a and b

Var = ((6-2+1)^2)/(12)

Var = (5^2)/(12)

Var = (25)/(12)