Question

To investigate the relation between hair color and eye color, the hair color and eye color of 5383 persons

was recorded. The data are given in the following table:

Hair Color

Eye Color | Fair/red Medium Dark/black

Light | 1168 825 305

Dark | 573 1312 1200

Eye color is encoded by the values 1 (Light), and 2 (Dark), and hair color by 1 (Fair/red), 2 (Medium),

and 3 (Dark/black). By dividing the numbers in the table by 5383 (the total sample size), the table

is turned into a joint probability distribution for random variables X (hair color) taking values 1 to 3

and Y (eye color) taking values 1 and 2.

(a) Determine the joint and marginal probability mass functions (pmf) of X and Y .

(b) Find out whether X and Y are dependent or independent.

Answer 1