Expected Value of a Continuous Random Variable

Introduction:

 The expected value is a measure of central location. For example of expected value continuous, your final grade in. this course will be the expected value of your performance in different tasks (quizes, exams, projects,...). The expected return of a lottery is equal to the average gain of that lottery. The expected value of a continuous random variable Y having probability density function f(y) is

               E(Y) = `int``y f(y)`dy

            For continuous random variables, the probability of an individual outcome in R(Y) is not defined, and R(Y) is uncountably infinite.

Expected Value of a Continuous Random Variable:

          The expected value continuous of a random variable Y, is denoted by E(Y) and may be interpreted as the long-term average value of Y. In the case of a discrete random variable, taking values y_1, y₂, y₃...

                E(Y) = EY_j P(Y=y_j)

          The random variable's expected value is average or central value. Here Y is defined as a random variable. If Y is a continuous random variable with probability density function f(y), then the expected value of Y is defined by:

                 µ = E(X)= x f(x) dx

           The expected value continuous or mean of a continuous random variable Y, denoted E(Y) (or, alternatively, µy), is the long run average of the values taken on by the random variable. For some random variables, E (│Y│) = ∞; and we say that the expected value does not exist.