Expectation and moments

This study gave an idea about “Expectation and moments” and about their role in the determination of conditional probability with the help of mathematical formulas. Probability is such a process that helps to find likelihood in any type of situation. This study is identifying real-life uses of conditional probability and gives some examples of these methods. This study discussed moments and expectations and their roles in Conditional probability. Besides this, the study is also discussed various types of conditional probabilities and properties of the method. This study also discusses the mathematical formula which is used to calculate the probabilities of the situation. 

Conditional probability and its example and use in real life

The “Conditional probability” is conceptualized as “the chance of the incident that can be occurred in the further time.” It can be calculated with the multiplication of the previous probability with the updated probability. Another definition of conditional probability is the chances of an event that can be happened in the near future so that the audience can manipulate it. An example of the method is the relationship of different individual events with each other and the acceptance of both events. Conditional probability is the opposite situation of the unconditional probability which is denied as the increased chance of an incident that can take place without concerning the outer environment so that the concerned person of the event can be ready with the measurement. A real-life example of conditional probability is seen in many areas such as “Politics, insurance, and calculus“. This probability is used in sports and in team building as this helps to estimate the performance of the members of the team of players. The estimation of performance by conditional probability helps them to improve their performance. Conditional probability is used in the “Bayes theorem” and “Python” as this method helps to calculate the future outcome of the investment.

Expectation and moments in Conditional probability and types of Probability

There are three main types of probability found and those are; “Theoretical Probability”, “Probability which is experimental”, “Probability which is Axiomatic”. The theoretical probability is defined as the process which calculates probability based on “reasoning behind probability”. Experimental probability is defined as the process which calculates probability based on the “Numbers of possible outcomes which are found by the experiments”. Axiomatic probability is defined as “a set of rules or axioms which applies to all types.” Those sets of axioms are known as the “Kolmogorov’s three axioms” and in this approach, there is a chance of quantification the situation. “Expectation or conditional expectation” is defined as the “expected value – this might refer to the value that can be expected in the probability graph for convenience” in conditional probability.

This helps to estimate the formulas which are applicable for the conditional probabilities of the one situation. The expectation of the conditions of a future situation is calculated with the help of conditional probability. “Expectations” are those conditions that are estimated by probability and may happen in the future.  In mathematics “Moments” is defined as the function that can be regarded as quantitative and that can be measured. Moments of the probability help to measure the relations between the data which are collected and help to estimate the expectation. 

Formula and properties of Conditional probability 

In mathematics conditional probability formula is; 

“P (A|B) = N (A∩B)/ N(B)”

In this formula “P (A|B)” stands for “the probability of occurrence of A given B has occurred.”

“N (A ∩ B)” stands for “the number of elements common to both A and B.”

“N (B)” stands for “the number of elements in B and it cannot be equal to zero.”

Conditional probability have three properties and those are, 

Property 1: “E and F be events of a sample space S of an experiment,” and in this situation, the formula for conditional probability is “P(S|F) = P(F|F) = 1”

Property 2: “A and B are any two events of a sample space S and F is an event of S such that P(F) ≠ 0, ” in this situation the result is “P((A ∪ B)|F) = P(A|F) + P(B|F) – P((A ∩ B)|F).”

Property 3: “P (A′|B) = 1 − P (A|B)”

Conclusion 

It is concluded that the study helped to develop a clear idea of “Expectation and moments” and their importance in “conditional probability”. This method helps to estimate the “expected” result of any situation by estimating previous results of a similar condition. Besides this, the study is given some real-life examples of the use of conditional probability like in politics and insurance. This process is very helpful as this is to estimates the expected future incidence and finds out the movements which are similar to the previous situation. Therefore it is concluded that this study developed a clear idea about “Expectation and moments” and their role in the determination of conditional probability.