This website houses notes from my studies at the University of Liverpool. If you see any errors or issues, please do open an issue on this site's GitHub.
This type of modelling is inspired by agile principles. Designing an ER Schema You should identify the basic components: Entity types. Relationship types. Attributes And for each of these components: Key attributes (unique for each identity). Cardinality and participation constraints of relationships. Different entity types. Strategies to ER Design Top-down...
Designing an ER Schema You should identify basic components: Entity types, relationship types, attributes: Key attributes. Cardinality and participation constrains of relationships. Different entity types. There are also weak entities such as tables or chairs. These simple objects don’t need individual identification and should be a child of the strong...
First Form If $P(A)>0$, then: \[P(B\vert A)=\frac{P(A\vert B)\times P(B)}{P(A)}\] Proof We have: $P(A\cap B)=P(A\vert B)\times P(B)$ $P(A\cap B)=P(B\vert A)\times P(A)$ Thus: \[P(A\vert B)\times P(B)=P(B\vert A)\times P(A)\] By dividing by $P(A)$ we get: \[P(B\vert A)=\frac{P(A\vert B)\times P(B)}{P(A)}\] Application - Diagnosis Assume a patient walks into a doctor’s office complaining of a...
In everyday language we refer to events that have nothing to do with each other as being independent. Definition Events $A$ and $B$ are independent if: \[P(A\cap B)=P(A)\times P(B)\] If $P(A)\neq 0$ and $P(B)\neq 0$, then the following are equivalent: $A$ and $B$ are independent. $P(B)=P(B\vert A)$ $P(A)=P(A\vert B)$ See...
Often we are interested in just part of the sample space. Conditional probability gives us a means of handling this situation. Example Consider a family chosen at random from a set of families having two children (but not having twins). What is the probability that both children are boys? A...
First Past the Post Example This example covers a first past the post election. This means whoever gets the most votes wins. We are aiming to make a function that performs this task: > winner ["red", "blue", "red", "red", "green"] > "red" Getting the Candidates First we need to figure...
Marks to Report Example This lecture covers a mini assignment example about converting a csv file containing students marks into a report containing the students averages. These are presented in the following format: aaa 70 65 67 60 bbb 55 60 55 65 ccc 40 40 40 40 ddd 80...
Disjoint Events Assume that $E _1,\ldots,E_n$ are mutually disjoint events. So $E_i\cap E_j=\emptyset$ whenever $i\neq j$. Then, \[P(\bigcup_{i\leq i \leq n}E_i)=\sum_{1\leq i\leq n}P(E_i)\] Example - Three Dice Suppose that I roll a fair die three times: $S$ is the set of dequences of lengh three over $\{1,\ldots,6\}$ (or $\{1,\ldots,6\}^3$). $P(x)=\frac{1}{6\times6\times6}=\frac{1}{216}$...
An event is a subset $E ⊆ S$ of the sample space $S$. The probability of the even $E$ is given by: \[P(E)=\sum_{x\in E}P(x)\] $0 ≤ P(E) ≤ 1$ for every event $E$ $P(\emptyset) = 0$ and $P(S) = 1$ Example - Fair Dice If I roll a die three...
Logic based knowledge representation and reasoning methods mostly assume that knowledge is certain. Often, this is not the case (or it is impossible to list all assumptions that make it certain): When going to the airport by car, how early should I start? 45 minutes should be enough from Liverpool...