Give the following definitions and examples. Please use different examples for each.
a) Illustrate what it means for two events to be mutually exclusive.
b) Give an example of two events which are mutually exclusive.
c) Give an example of two events which aren't mutually exclusive.
d) Illustrate what it means for two events to be independent.
e) Give an example of two events which are independent.
f) Give an example of two events which aren't independent.
g) Illustrate what it means for two events to be "correlated."
h) Give an example of two events which are correlated.
i) Give an example of two events which aren't correlated.