Sets and events you need to know for data science

Read about sets and events for free in just 3 minutes

1. Sets and Events :

• Sets are used to eliminate duplication
• Event : Set of outcomes, If a set is empty it is called an empty set or null set denoted by Ø .

Non-Empty Set :

• A non-empty set can be finite or infinite

Example :

• X ∈ A (X in A)
• The above tells that X is the element of set A
• Where A -is set, X -is an element

(OR)

• A ∋ X (A contain x)
• Where A -is set, X -is an element.

Representing not a part of a set:-

• X ∉ A ( which means X is an element set not in A )
• A ∌ X ( which means A does not contain X )

2. Multiple Element in Set :

• A multiple-element in a set can be represented with the symbol ∀ (for all/any)
• Example : ∀ X ∈ A ( it denotes that for all the member of x is in A )

3. Colon :

1. The colon can be denoted by : ( ‘ : ’ means such that or so )
2. : indicates a group of specific elements in the set.
3. Example : ∀ X ∈ A : X is even

4. Subset :

• A set that contains (holds) another subset(set) can be denoted by ⊆
• Example: A ⊆ B [A is the subset of B]

5. Intersection :

• Intersection represents all the favourable outcomes between two events
• Notation: A ⋂ B

6. Union of Sets :

• A combination of all outcomes preferred like either A or B (or both)
• Notation: A ∪ B
• Formula: A ∪ B = A + B -A ⋂ B

7. Mutually Exclusive Sets :

Basically mutually exclusive set is a set, which does not allow to have overlapping elements, like circles never intersect.

Complements :

First, if a set consists of all odd numbers then its complement would be set of all even number.

Complements are always mutually exclusive, but not all mutually exclusive sets are complements

8. Independent Events :

The theoretical probability remains unaffected by other events like tossing a coin [always have 50% chance of getting tails]

9. Dependent Events :

The probabilities of dependent events vary as conditions change.

• So,the probability of an event changes depending on the information we have.

10. Conditional Probabilities :

The chance of an event occurring, assuming a different one has already happened(known or exist)

Additive Law :

The probability of the union of two sets is equal to the sum of the individual probabilities of event minus probability of their intersection.

Multiplication Law :

The probability of the union of two sets is equal to the sum of the individual probabilities of event multiply probability of their intersection.

Bayes Law :

Simply Bayes law is also called as Bayes rule or Bayes theorem. We can get the bayesian theorem by applying conditional probability to Bayes law.

read more articles :

How Combinatorics used in data science

What are the basics of Probability you need to know for data science

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