Question

Please share your understanding of Expected Value in your own words?

The mean of a probability distribution is often called the expected value of the
distribution. This terminology reflects the idea that the mean represents a “central
point” or “cluster point” for the entire distribution. Of course, the mean or expected
value is an average value, and as such, it need not be a point of the sample space.
The standard deviation is often represented as a measure of risk. A larger standard
deviation implies a greater likelihood that the random variable x is different
from the expected value m.

Answer 1

In probability theory the expected value of a random variable is actually the arithmetic mean of large no of observations of that random variable. It can be expressed as the weighted average of all the values that the r.v takes. Generally the relative frequencies or the corresponding probabilities are taken as the weights. It's one of the measures of the central tendency of a given data set.