Q.6 Which one 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}

Q.6 Which one 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) $E\left[g\right(x\left)\right]={\int }_{-\mathrm{\infty }}^{\mathrm{\infty }}g\left(X\right)dX$

(b) $E\left[g\right(x\left)\right]={\int }_{-\mathrm{\infty }}^{\mathrm{\infty }}g\left(X\right)f\left(X\right)dX$

(c) $E\left[g\right(x\left)\right]={\int }_{-\mathrm{\infty }}^{\mathrm{\infty }}{g}^{\ast }\left(X\right)dX$

(d) $E\left[g\right(x\left)\right]={\int }_{-\mathrm{\infty }}^{\mathrm{\infty }}\left[\frac{g\left(X\right)}{f\left(X\right)}\right]$