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In probability theory, the expected value (also called expectation, expectancy, expectation operator, mathematical expectation, mean, expectation value, or first moment) is a generalization of the weighted average.
In quantum mechanics, the expectation value is the probabilistic expected value of the result (measurement) of an experiment. It can be thought of as an average of all the possible outcomes of a measurement as weighted by their likelihood, and as such it is not the most probable value of a measurement; indeed the expectation value may have zero probability of occurring (e.g. measurements which ...
The parameter is the mean or expectation of the distribution (and also its median and mode), while the parameter is the variance. The standard deviation of the distribution is (sigma).
When two random variables are statistically independent, the expectation of their product is the product of their expectations. This can be proved from the law of total expectation : E ( X Y ) = E ( E ( X Y ∣ Y ) ) {\displaystyle \operatorname {E} (XY)=\operatorname {E} (\operatorname {E} (XY\mid Y))}
In probability theory, the conditional expectation, conditional expected value, or conditional mean of a random variable is its expected value evaluated with respect to the conditional probability distribution. If the random variable can take on only a finite number of values, the "conditions" are that the variable can only take on a subset of ...
The red population has mean 100 and variance 100 (SD=10) while the blue population has mean 100 and variance 2500 (SD=50) where SD stands for Standard Deviation. In probability theory and statistics, variance is the expected value of the squared deviation from the mean of a random variable.
These are the expected value (or mean) and standard deviation of the variable's natural logarithm, (), not the expectation and standard deviation of itself. Relation between normal and log-normal distribution.
The mean is the probability mass centre, that is, the first moment. The median is the preimage F −1 (1/2). The mean or expected value of an exponentially distributed random variable X with rate parameter λ is given by E [ X ] = 1 λ . {\displaystyle \operatorname {E} [X]={\frac {1}{\lambda }}.}