IV. Statistical Independence
If joint probability of two events E1 and E2 is equal to the product of marginal probability of E1 and E2, then E1 and E2 are said to be statistically independent. Mathematically, two events E1 and E2 are statistically independent if:
P(E1⋂E2) = P(E1).P(E2)
If this relationship does not hold true, events E1 and E2 are statistically not independent.
Example:
A number is selected randomly from the first n natural numbers. Let E1 be the event that it is divisible by 2, and E2 be the event that it is divisible by 3. Show that the events are statistically independent if n=96.
Solution:
When n=96,
and
Here,
as
Hence, events E1 and E2 are statistically independent.