Statement
The result is that two independent events become conditionally dependent (negatively dependent) given that at least one of them occurs. Symbolically:
- if 0 < P(A) < 1 and 0 < P(B) < 1,
- and P(A|B) = P(A), i.e. they are independent,
- then P(A|B,C) < P(A|C) where C = A∪B (i.e. A or B).
In words, given two independent events, if you only consider outcomes where at least one occurs, then they become negatively dependent.
Read more about this topic: Berkson's Paradox
Famous quotes containing the word statement:
“The most distinct and beautiful statement of any truth must take at last the mathematical form.”
—Henry David Thoreau (1817–1862)
“Children should know there are limits to family finances or they will confuse “we can’t afford that” with “they don’t want me to have it.” The first statement is a realistic and objective assessment of a situation, while the other carries an emotional message.”
—Jean Ross Peterson (20th century)
“The new statement is always hated by the old, and, to those dwelling in the old, comes like an abyss of skepticism.”
—Ralph Waldo Emerson (1803–1882)