Now, my definition has changed for adaptation, and, to my research purposes and future ambition. I have to choose one, not balanced everything and my hobbies.
It has been a struggle since I got my Honours, I feel lucky for me to have the chance to work with the one whom I never seen or met or even work together before. And I felt that it is my honour and pleasure to work with them and they are my lifesaver from last year (not a disaster but a bad moment to look at it). I have to say each time
Giving some tutorial for adapting and testing, I would want to test it out some of the basic and advanced things that we will focus on that.
In basic version:
We also have
Fractions: $\frac{a+b}{c}$
Make it a single equation line like: $$\frac{a+b}{c}$$
Decide an experiment random with S as sample space. A function X which assigns to every outcomes $s \in S$, a real number X(s) = x is called a random variable.
When we toss a coin. S the sample space {H, T}. Defining a random variable X as:
A random variable called X, which is able to take on a countable number of values is a discrete random variable, which probability
$$ P(B|A) = \frac{P(A|B)P(B)}{P(A)} $$
$P(A|B) = \frac{P(A\cap B)}{P(B)}$, and, $P(B|A) = \frac{P(B\cap A)}{P(A)}$,$P(A\cap B)$same as $P(B \cap A)$
$$ P(A|B) \cdot P(B) = P(B|A) \cdot P(A) = P(A\cap B) $$ $$ P(A|B) \cdot P(B) = P(B|A) \cdot P(A) $$
Finally: $P(B|A) = \frac{P(A|B) \cdot P(B)}{P(A)}$
P(B) is the prior
P(A|B) is the likelihood
When it comes to two events A and B, if P(B) > 0, then the probability of A given B is
$$ P(A|B) = \frac{P(A\cap B)}{P(B)} $$
Rolling a dice with two events:
The sample space for rolling a dice is: $\{1,2,3,4,5,6\}$
Based on the formula of $P(
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