If you are playing game that includes dice what are the chances that you are having a 6 in the first three attempts. Or what would be the chances that you are going to have 1 instead in the first 6 attempts? These all questions and probability of you having a specific number on your dice are related to Expected Value of statistics and probability theory.
To learn more about expected value, calculation of expected value, difference between mean and expected value and expected number in probability read on the article below.
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What is Expected Value?
A center or mean value has indicated by the expected value or population means of the random variable. It provides a fast intuition of a random variable’s behavior without knowing whether it is discreet or continuous. For the variable distribution, the variance is a significant summary value.
Consequently, two random variables with the same value might have distinct distributions of probability. The distribution shape has also affected by other descriptive metrics such as standard deviation. The expected value may represent as E(X) for the random variable X.
However, to define it accurately we would say, for a particular random variable, the expected value is an average value when an experiment is repeated several times. Or the “theoretical mean” of a random variable can be used to define it in other words. As it is not a sample data-based measure and depends on the population. It’s a parameter, thus, and not static.
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What is the Expected Number in Probability?
The expected number, expectation or mathematical expectation or EV or mean in probability refers to the value of the random variable that is anticipating by repeating the random variable procedure infinite times and taking an average of the values received.
The weighted average of all possible values is the expected value, according to the probability theory. The weights utilized in calculating this average are the probabilities for a discrete random variable or values of a probability density function for a continuous random variable.
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Are Mean and Expected Value Same things?
As discussed above a random variable’s expected value is simply the arithmetic mean that has predicted. The expected value for a discreet random variable however is the weighted average of the random variable’s possible values, with weights being the probabilities to occur.
That’s why it is sometimes calling as the X mean and the words might use in this context unteachable. Whilst the mean is the simple average of all values that you can calculate with a mean finder. On the other hand, the expected value is the average value with respect to its random weight.
In mean we don’t take a average of the variables with respect to its weight. That we can calculate in expected. Thus, we can say that expected value in probability and mean are not same things.
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How to Calculate Expected Value?
The formula for expected value in statistics as well as in probability is E(X) = ΣX * P(X), or the summation of all gains multiplied by individual probabilities. Two components on which the expected value is dependent include, i.e. how much you can expect to gain and how much you can expect to lose.
For example, if X is a random variable, the expected value EX of X is generally define as the sum and/or integrated value on X of X * P(X), where X * P(X) is the probability mass function or probability density.
You can try online expected value of probability distribution calculator to find it online.
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Wrapping Up
Therefore, the expected sometimes called the “mean” value of a random variable “X”. It is the average repetitive value of the same experiment. This means that X can take on a weighted average of all possible values. With each value weighed according to the probability. It shows in the experiment or sampling. However, the process of expected value calculation includes taking mean. But we can’t call it is as the exact mean as we take a weighted average. The symbol E(X) indicates a random value’s (X) expected value.
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