Which of the following gives the average value or expectation of the function g(X) of the random variable X?
(Given f(X) is the probability density function)

A. $$E\left[ {g\left( X \right)} \right] = \int\limits_{ - \infty }^\infty {g\left( X \right)dx} $$

B. $$E\left[ {g\left( X \right)} \right] = \int\limits_{ - \infty }^\infty {g\left( X \right)f\left( X \right)dx} $$

C. $$E\left[ {g\left( X \right)} \right] = \int\limits_{ - \infty }^\infty {{g^ * }\left( X \right)dx} $$

D. $$E\left[ {g\left( X \right)} \right] = \int\limits_{ - \infty }^\infty {\frac{{g\left( X \right)}}{{f\left( X \right)}}dx} $$

Answer: Option B