i like maths when i was young,but i need to record them. so i am writing with some demos of python
if two events, a and b are independent then the joint probability is
<dl><dd> </dd></dl>
for example, if two coins are flipped the chance of both being heads is
in python
output:
# & find the objects the same in set
if either event a or event b or both events occur on a single performance of an experiment this is called the union of the events a and b denoted as:
.
if two events are mutually exclusive then the probability of either occurring is
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for example, the chance of rolling a 1 or 2 on a six-sided die is
# | find all the objects the set has
if the events are not mutually exclusive then
proved
for example:
let me show u some others :
if u r tired , please have a tea , or look far to make u feel better.if u r ok, go on!
conditional probability is the probability of some event a, given the occurrence of some other event b. conditional probability is written:
,
some authors, such as de finetti, prefer to introduce conditional probability as an axiom of probability:
①
given two events a and b from the sigma-field of a probability space
with p(b) > 0, the conditional probability of a given bis defined as
the quotient of the probability of the joint of events a and b, and the
probability of b:
②
the ①② expressions are the same. maybe u can remember
one , the other will be easy to be coverted.so i am going to tell an
excemple to let u remmeber it(them):
“the phone has a power supply (b), the phone can be used to call others(a).”
one →
: when the phone has a full power supply , u can call others.
two →p(b): has a power supply
three = one + two → u can call others about your love with others.
do u remember it?
“路漫漫其修遠兮,吾将上下而求索”
cya soon. we meet a big mess called the total probability and bayes .
the total probability
bayes (thomas, 1702-1761,) ;
if u wanna talk with me , add the follow: