(a) Prove that the energy of the Gaussian pulse is given by $1/26 \pi…

Question

(a) Prove that the energy of the Gaussian pulse is given by $1/26 \pi$ where $6$ is the standard deviation of the pulse.

(b) Which of the following functions satisfy the properties of PDF and why?

(i) $f_x (x) = \frac{1}{x (1+x^2)}$

(ii) $f_x (x) = x \text{ for } x < 1$

(iii) $f_x (x) = (8-x)/6$ . ( 10, 10 )