Probability plays an important role in estimation of various statistic and parameters, & hence it is imperative to understand probability concepts before moving forward. Whenever you are interacting with any problem related to statistic, there is always a "chance" that your results are acceptable or within a acceptable range.
A Hypothesis testing is solely based on the chance that some statement made is supported by the results or not. Here also we have difference probability distributions that comes into picture.
Probability: A probability is a measure of chance of a favorable outcome, it can be calculated as ratio of no. of all favorable outcomes to total no. of outcomes. This is an important concept as it helps in predicting the chances of a future event, which is at the core of any predictive or prescriptive data analysis.
Many of such events are not falling in the definition of probability but still can be figured, using probability based naive bayes theorem & other advanced probability concepts.
Probability = No. of favorable outcomes
Total no, of outcomes
It can be represented as
P[x] Ļµ [0,1] , it means probability of any event 'X' belongs to a set of values between 0 & 1 including both.
To understand the concept of probability in simpler manner, let's take an example of a railway station, from where a passenger can go only in 2 direction, either North or South. You are standing near ticket counter & a passenger comes to ticket window, what is the probability or chances that he boards a Northbound train.
Ok lets count our favorable outcomes = 1 i.e. northbound train
& total outcomes = 2 i.e. northbound or southbound train
So the chances or the probability of this passenger to take a Northbound train is
= No. of favorable outcomes = 1 = 0.5 or 50%
Total no, of outcomes 2
So there are 50% chance or 1/2 or 0.5 probability of him boarding a northbound train.
Please consider that a passenger after taking a ticket will anyhow board the train, going to his destined direction.
Now does that mean that if there are 2000 passengers coming to station then 1000 passenger will board Northbound train and other 1000 passenger a Southbound train?
Not exactly! The probability is just a measure which defines a chance for a favorable outcome.
Hope this clears your doubt as the probability does not mean that out of 100 passenger, if 50 takes a northbound train then other 50 are bound to take a southbound train, that never happens. But repeating this experiment a large no. of times will return a no. close to 0.5. & if we keep on doing this experiment of asking infinite no. of passengers about their destination( northbound or sothbound) an infinite no. of times then we will get this ratio as 0.5.
There are certain terminalogies which one should be aware of while moving around Probability.
Experiment: An experiment is the occurrance of a random event.
Sample space : This is a set of all possible outcome of an experiment.
Probability: A probability is a measure of chance of a favorable outcome, it can be calculated as ratio of no. of all favorable outcomes to total no. of outcomes. This is an important concept as it helps in predicting the chances of a future event, which is at the core of any predictive or prescriptive data analysis.
Many of such events are not falling in the definition of probability but still can be figured, using probability based naive bayes theorem & other advanced probability concepts.
Probability = No. of favorable outcomes
Total no, of outcomes
It can be represented as
P[x] Ļµ [0,1] , it means probability of any event 'X' belongs to a set of values between 0 & 1 including both.
To understand the concept of probability in simpler manner, let's take an example of a railway station, from where a passenger can go only in 2 direction, either North or South. You are standing near ticket counter & a passenger comes to ticket window, what is the probability or chances that he boards a Northbound train.
Ok lets count our favorable outcomes = 1 i.e. northbound train
& total outcomes = 2 i.e. northbound or southbound train
So the chances or the probability of this passenger to take a Northbound train is
= No. of favorable outcomes = 1 = 0.5 or 50%
Total no, of outcomes 2
So there are 50% chance or 1/2 or 0.5 probability of him boarding a northbound train.
Please consider that a passenger after taking a ticket will anyhow board the train, going to his destined direction.
Now does that mean that if there are 2000 passengers coming to station then 1000 passenger will board Northbound train and other 1000 passenger a Southbound train?
Not exactly! The probability is just a measure which defines a chance for a favorable outcome.
Hope this clears your doubt as the probability does not mean that out of 100 passenger, if 50 takes a northbound train then other 50 are bound to take a southbound train, that never happens. But repeating this experiment a large no. of times will return a no. close to 0.5. & if we keep on doing this experiment of asking infinite no. of passengers about their destination( northbound or sothbound) an infinite no. of times then we will get this ratio as 0.5.
There are certain terminalogies which one should be aware of while moving around Probability.
Experiment: An experiment is the occurrance of a random event.
Sample space : This is a set of all possible outcome of an experiment.
Sample point: Sometimes refered to as sample, this is a possible outcomes of an experiment.This is a necessary unit subset of Sample space.
Event:This is a set of one or more sample points or possible outcomes.
Mutually Exclusive Event: An event is said to be mutually exclusive if occurrance of an outcome causes non-occurrance of other events.
Non-Mutually Exclusive Event: An event is said to be mutually exclusive if occurrance of an outcome causes non-occurrance of other events.
Exhaustive Events:
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