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

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Correct Answer: Option B

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Which of the following gives the average value or expectation of...

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)

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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)