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Useful Facts to Know About Expected Value and Summation

Expected Value

The expected value is also known as the mean, average, or first moment. The expected value formula is often useable in probability as well in statistics to calculate the expected value of a random variable X, which is follow by E(x). 

To describe this concept mathematically, it may be defined as the expected value, which is equal to the total of each potential event multiplied by its associated probability and then added together. 

The expected value is equal to the arithmetic mean of all the possible results in case all the results’ probabilities are equal. Using the summation or sigma symbol the expected value formula to calculate EV, it will;

Expected Value = Σ x(probability of x happening)

You may calculate the expected value by using the expected number calculator, as it is the top-rated tool that provides you precise answers as well as steps for detailed learning and understanding.

Useful Facts About Expected Value

According to the above-mentioned information, the expected value of X is the mean of the discrete random variable X. And the expected value of X is representing by a symbol of E (X). However, to calculate the mean of a discrete random variable, E(X) use the following formula:

E(X) = Σ [ xi * P(xi)]

The formula thus implies; the total function is the sum of all the terms and then multiply them by their probabilities. Moreover, there is a corresponding random variable value expressed as Xi), and the probability of that random variable value denoted as P(Xi) that equals the resultant value “i”. Some useful facts to know about expected value are as follow:

  • When calculated, the expected value is equal to the product of the probability of each result and the outcome.
  • A rapid and direct understanding of the behaviour of any random variable can obtain by using the formula
  • As one of the most often used financial metrics in finance, the expected value predicts the expected values regarding upcoming investment
  • Moreover, It mostly use as a number of disciplines, to predict the anticipated values.

Summation

For the sum of a series of numbers terms, the summation will use as. For instance, to calculate the sum of, 2, 3, 4, 5, 6, 7 i.e. 2+3+4+5+6+7 the result comes out to be 27. In this example, the 2+3+4+5+6+7 is a specific sequence of numbers while “27” is the summation of this sequence.

Moreover, the upper sum example may write in a simple form utilizing a so-called sigma notation. Through sigma notation, the above sequence will:

Thus the summation notation is a way of expressing sums in a concise way and to represent the summation Sigma a capital Greek letter is used. you may calculate the sum of long and defined series by using a summation notation calculator

Useful Facts About Summation

If you look at the representation of a sigma notation above, you will see the several smaller letters spread all around it. i shows us which sequence or series we add together, this i is known as the index of summation. 

It may be an individual word or a polynomial or a series. The 2 is the lower limit whereas the 7 is the upper limit of summation. The sigma notation helps to determine the sum that can read out loud. For instance, the before mentioned summation example may read as, find the sum of values from 2 to 7 in a series. 

The summation, however, is readable from bottom to top, the lower limit tells from which value we have to begin summation. While the upper bound or upper limit mentions the last value in the series to be sum. In order to define at a closed interval, the definite integral of a continuous function of a single variable. The summation notation can be defined as, if in the expression, f(i) is a function with i, it will mean and illustrates then;

As we learnt the summation represents the long series and sequence of numbers to add in a simple and concise manner, however, summation can also use, to sum up, geometric series comprising repeating decimals. Moreover, we can also find the area under the curve using the summation rules. Because integration is also a process of summation

The general summation rules are :

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