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MLAIT
3y ago
Hey Developer’s, I’m back with a new topic which is Bayes Theorem in the series of statistics foundations.
Quick Refresher
Law of Total Probability:
If B1,B2,B3,⋯ is a partition of the sample space S, then for any event A we have,
So, let’s get started …
Bayes Theorem
It is a way of finding a probability when we know certain other different probabilities. Basically calculates the probability of an event, based on the prior knowledge of conditions that might be related to the event.
where A and B are events and P(B) ≠ 0.
P(A|B) is a conditional probabi ..read more
MLAIT
3y ago
Hey Developer’s, I’m back with a new topic which is Law of Total Probability in the series of statistics foundations.
Quick Refresher
Multiplicative Law
The probability of intersection of two events A and B is
P(A∩B) = P(B)P(A|B) = P(A)P(B|A),if values swapped
If these events are independent, then P(A∩B) = P(A)P(B)
Additive Law
Probability of a union of events, P(A U B) = P(A) + P(B) – P(A∩B)
If A and B are mutually exclusive,P(A∩B) = 0 and
P(A U B) = P(A) + P(B)
So, let’s get started …
Law Of Total Probability
Let’s start with an example, if you have bought three pens, prices are P1 = Rs. 10 ..read more
MLAIT
3y ago
Hey Developer’s, I’m back with a new topic which is Multiplicative and Additive Law Of Probability in the series of statistics foundations.
Quick Refresher
If any of the following condition holds, then the two events A and B are independent,
P(A|B) = P(A)
P(B|A) = P(B)
P(A∩B) = P(A)P(B)
If none of these condition holds, the events are dependent and if any one of the condition holds from this the events are independent.
So, let’s get started …
Multiplicative Law Of Probability
As we learned before the formula of conditional probability,
P(A|B) = P(A∩B) / P(B)
The probability of intersection o ..read more
MLAIT
3y ago
Hey Developer’s, I’m back with a new topic which is Independence Of Events in the series of statistics foundations.
Quick Refresher
Conditional probability is defined as the likelihood of an event or outcome occurring, based on the occurrence of a previous event or outcome.
Unconditional Probability is defined as the likelihood that an event will take place independent of whether any other events take place or any other conditions are present.
So, let’s get started …
Independence of Events
Two events A and B are independent if events do not influence one another.
If any of the following cond ..read more
MLAIT
3y ago
Hey Developer’s, I’m back with a new topic which is Conditional and Unconditional Probability in the series of statistics foundations.
Quick Refresher
Probability of Union Of Events – Statistics Part 15
So, let’s get started …
Let’s Understand With Example, First
Unconditional Probalility : Probability that it will rain today giving no additional information.
Conditional Probability : Probability that it will rain today given it’s been raining an enitre week.
Here you can see that the unconditional probaility does not depends on other obervations, but the conditional probability depends on the ..read more
MLAIT
3y ago
Hey Developer’s, I’m back with a new topic which is Probability of Union Of Events in the series of statistics foundations.
Quick Refresher
A multinomial coefficient is not just of separating two groups of elements but actually separating several groups,more than 2.
So, let’s get started …
Probability of a Union Of Events
We also know that for a set of disjoint events A(i),
P(U A(i)) = Submission
For every two (not necessarily disjoint(Which does not overlap)) events A and B, P(A ⋃ B ) = P(A) + P(B) – P(A ⋂ B)
This can be extended to 3 or more events, Ex: P(A⋃B⋃C) = P(A) +P(B) + P(C) – {P(A ..read more
MLAIT
3y ago
Hey Developer’s, I’m back with a new topic which is Multinomial Coefficients in the series of statistics foundations.
Quick Refresher
A binomial coefficient equals the number of combinations of k items that can be selected from a set of n items.
So, let’s get started …
Multinomial Coefficients
It’s not just of separating two group of elements but actually separating several groups ,more than 2
Example: 10 students need to from 3 groups consisting of 4,3 and 3 members repectively.How many ways can students be assigned to these groups ?
Solution = First Group : Choose 4 students out of 10, 10C4 ..read more
MLAIT
3y ago
Hey Developer’s, I’m back with a new topic which is Binomial Coefficients in the series of statistics foundations.
Quick Refresher
Combinatorics is a branch of mathematics concerning the study of finite or countable discrete structures.
C(n,k) = P(n,k)/k! = n!/k!(n-k)!
So, let’s get started …
Binomial Coefficients
A binomial coefficient equals the number of combinations of k items that can be selected from a set of n items.
If your observations are independent, each represents one of two outcomes (think: success and failure), your number of trials is fixed and the probability of success ..read more
MLAIT
3y ago
Hey Developer’s, I’m back with a new topic which is Combinatorics in the series of statistics foundations.
Quick Refresher
Given a set of elements, all distinct arrangements of these elements are called the permutation of a set.
The number of ways you can arrange N elements out of N possibilities is…
P(n,n) = N X (N-1) X (N-2) X …. X 2 X 1 = N! permutations
So, let’s get started …
Combinatorics
Combinatorics is a branch of mathematics concerning the study of finite or countable discrete structures.
Combinatorial Methods
Given a bag of balls B = {R,G,B,W,O}
If we pull out 2 balls after replacem ..read more
MLAIT
3y ago
Hey Developer’s, I’m back with a new topic which is Permutations in the series of statistics foundations.
Quick Refresher
Counting Sample Points: It means how many sample points are there in the sample space.
So, let’s get started …
Permutations
Given a set of elements, all distinct arrangements of these elements are called the permutation of a set.
The number of ways you can arrange N elements out of N possibilities is…
P(n,n) = N X (N-1) X (N-2) X …. X 2 X 1 = N! permutations
N! = “N factorial” = a product of all numbers from N down to 1
Assumes N is a non-negative integer
By definition,0 ..read more