Question

For the following prob. density function, given by:

F ₓ (x) = a/π 1/a ² + x ² a > 0, all x s
Using the Cauchy residue method , determine the characteristic function Φₓ ω

Answer 1

To find the characteristic function Φₓ ω using the Cauchy residue method, we need to evaluate the integral of the probability density function Fₓ(x) multiplied by eⁱᵧˣ around a closed contour in the complex plane. However, the information provided does not contain the necessary data to perform the calculations required to find the characteristic function. Please provide additional information or clarify the question so that we can assist you further.

Step-by-step explanation:

The characteristic function, Φx(ω), represents the Fourier transform of the probability density function.

To find the characteristic function Φx(ω) using the Cauchy residue method, we need to evaluate the integral of the probability density function Fx(x) multiplied by eiωx around a closed contour in the complex plane.

However, the information provided does not contain the necessary data to perform the calculations required to find the characteristic function. Please provide additional information or clarify the question so that we can assist you further.