This is only true if A and B are independent. You can never assume A and B are independent. You must either know it or prove it.
This is always true for two events A and B. The left hand side P(A divides B) is the probability that A will happen given that B has happened, often written as A given B or A conditional on B. If A and B are independent then
so
This is always true.
The above equations are very useful when working with Venn diagrams.
Correlation Coefficients and Regression Lines
where
If the equation of a regression line of
on
is given by
then
and
The unbiased estimate of the standard deviation of a random variable
found from a list of n numbers
is given by
where
If the expectation value – often called the mean, average, and written
or
– of a random variable
is given by
and
then
and
and
for all distributions, but if the distribution is continuous we may use
and
and
for a continuous distribution etc.
for a continuous distribution.