Difference b/w Mutual Exclusivity and Statistical Independence

Hi Team,

Though I understand terms Mutual Exclusivity and Statistical Independence but easily get confused between them.

Can anyone help in giving example of Mutual Exclusive events which are not Statistical Independence and vice-versa.

Regards,

Jagjit

In layman's terms, two events

In layman's terms, two events are mutually exclusive if they cannot occur at the same time (i.e., they have no common outcomes). An example is tossing a coin, which can result in either heads or tails, but not both. Both outcomes can't happen simultaneously.

Statistical independence is that the occurrence of one event makes it neither more nor less probable that the other occurs. For example:

• The event of getting a 6 the first time a die is rolled and the event of getting a 6 the second time are independent.

• By contrast, the event of getting a 6 the first time a die is rolled and the event that the sum of the numbers seen on the first and second trials is 8 are dependent.

Regards

Source - Wikipedia.org

I understand your point but as you mentioned that "The event of getting a 6 the first time a die is rolled and the event of getting a 6 the second time are independent." Ain't these 2 events mutually exclusive too as they cannot occur at the same time?

No its not mutually exclusive

No its not mutually exclusive since both times you can get 6. It would be mutually exclusive if you get 6 one time and next time you cannot get 6. Like tossing the coin, getting heads or tails is mutually exclusive event, you cannot get both at the same time, however getting heads once does not mean you will not get heads again, so its statistically independent.

When you play lotto and if a number is called out than that number cannot be called again, so that event is statistically dependent