Let X be a Poisson random variable with mean λ. Show that for k = 1, 2, . . . , Use this conditional probability mass function to show that Use a computational software program to simulate an Airy...

Let X be a Poisson random variable with mean λ. Show that for k = 1, 2, . . . ,

Use this conditional probability mass function to show that

Use a computational software program to simulate an Airy image function for typical values of the numerical aperture na and the wavelength λ.