Conditional probability, statistics and their relation
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Posted On :
Sep-16-2011
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Article Word Count :
544
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Friends, today we are going to learn the basic concepts behind conditional probability and how it will help in statistical calculations.
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Friends, today we are going to learn the basic concepts behind conditional probability and how it will help in statistical calculations. For understanding conditional probability, we need to know what probability is. So, in simple if we say an event is probable it means that it may happen and it may not happen, so probability is a way of telling or expressing a knowledge that an event will occur or has occurred. Probability theory plays an important role in various human activities that involves the analysis of a large set of data.
So, conditional probability is the probability of an event occurring given that another event has already occurred. The Mathematical view of this statement comes with the following equation that an event X occurs, given that an event T has already occurred.
P (T|X) = P(X and T) / P(X)
P(X/T) = Probability of occurrence of event X when the event T as already occurred and P (T/X) = Probability of occurrence of event T when the event X as already occurred
Besides this there is another method to calculate conditional probability known as Baye's formula. It states that the probability of event T is the sum of the conditional probabilities of event T given that event X has or has not occurred. Mathematical expression for the above is : P(T) = P(T|X)P(X) + P(T|Xc)P(Xc)
And for the two independent events (for event X and event T) the expression is:
P(T)P(X) + P(T)P(Xc) = P(T)(P(X) + P(Xc)) = P(T)(1) = P(T)
Let us take an example to understand the basic behind the conditional probability problems: calculate the probability of getting a head when we toss a coin.
So, we all know coin has two faces either head or tail. So when toss happen only one side of coin is visual. So the probability of getting a head is:
1 - ½ = ½. So the probability of getting a head is 0.5 or ½.
Statistics, on the other hand is the practice or science of collecting and analyzing numerical data in large quantities. It is basically a study of the collection, organization, analysis and interpretation of the data. So, the two things probability and statistics together plays an important role in finding out measures of central value, measures of spread of different data and this helps in comparing of two data. Now we now know how probability and statistics can help in the analysis of data.
For example if we have to calculate the central value for 4 and 6: It is calculated as (4+ 6)/2 = 10/2 = 5. Here is another instance where we have to calculate a range for 9, 11, 4, 8, 5, 6, 2000, the lowest value is 5 and the highest value is 2000 then the range is: 2000 – 5 = 1995.
Statistics is the science which deals with variations, randomness and chance. It is different from other science as others works or studied on exact deterministic mathematics values. In a lot of statistical analysis and experiments, the result depends on probability distributions as probability plays an important part in statistical analysis, statistical analysis uses probabilities and probability calculations uses statistical analysis.
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Article Source :
http://www.articleseen.com/Article_Conditional probability, statistics and their relation_82704.aspx
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Author Resource :
TutorVista is the #1 portal for learning statistics online. The tutors working with us are great in explaining Probability in best possible way.
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Keywords :
Conditional probability, statistics, Probability,
Category :
Reference and Education
:
Homeschooling
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