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Does expected value always exist?
Note that the expectation does not always exist (if the corresponding sum or integral does not converge, the expectation does not exist. One example of this situation is the Cauchy random variable).
Is the expected value of a random variable is always finite?
It is not surprising that the expected value is infinite when infinity is a possible value. However, the expected value can be infinite, even if the random variable is finite-valued.
Can expected value not exist?
In any case, the expected value of X may not exist because the sum or the integral may not converge. However, unless otherwise noted, whenever we write an expected value, we are assuming that it exists. The mean is the center of the probability distribution of X.
How do you know if a value does not exist?
Here are the rules: If the graph has a gap at the x value c, then the two-sided limit at that point will not exist. If the graph has a vertical asymptote and one side of the asymptote goes toward infinity and the other goes toward negative infinity, then the limit does not exist.
Does the mean always exist?
Mean of a probability distribution The mean need not exist or be finite; for some probability distributions the mean is infinite (+∞ or −∞), while for others the mean is undefined.
Which is the expected value of a random variable?
Expectations of Random Variables 1. The expected value of a random variable is denoted by E[X]. The expected value can bethought of as the“average” value attained by therandomvariable; in fact, the expected value of a random variable is also called its mean, in which case we use the notationµ.
How to calculate the expected value of a discrete variable?
For a discrete random variable, the expected value, usually denoted as μ or E (X), is calculated using: μ = E (X) = ∑ x i f (x i) The formula means that we multiply each value, x, in the support by its respective probability, f (x), and then add them all together.
How to calculate the variance of a random variable?
The variance of a discrete random variable is given by: The formula means that we take each value of x, subtract the expected value, square that value and multiply that value by its probability. Then sum all of those values. There is an easier form of this formula we can use.
How to calculate the expected value of X?
The formula means that we take each value of x, subtract the expected value, square that value and multiply that value by its probability. Then sum all of those values. There is an easier form of this formula we can use.