The expected value of a random variable is
the mean value over an infinite number of observations of the variable. So, correct answer is option (b).
What is excepted value ?
The expected value of a random variable is denoted by E[X]. The expected value can be thought of as the “average” value attained by the random variable or in fact, the expected value of a random variable is also called its mean, in which case we use the notation µX. Now, we check the options and drive write statement.
a)The highest probability value is not the “expected” value of a random variable.
b)The “expected value” of a random variable is also known as the “mean” value of the variable over an “infinite” number of observations.
c) The largest value that will ever occur is the largest observed value, not a random variable mean.
d) The “mode” of a random variable is the most common value over an “infinite” number of observations of the variable.
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Complete question:
The expected value of a random variable is the
a. value that has the highest probability of occurring.
b. mean value over an infinite number of observations of the variable.
c. largest value that will ever occur.
d. most common value over an infinite number of observations of the variable