Penumbrol imaging is a technique used by nuclear engineers for imaging objects (e.g., X-rays and lasers) that emit high-energy photons. In IEICE Transactions on Information & Systems (Apr. 2005), researchers demonstrated that penumbrol images are always degraded by noise, where the number x of noise events occurring in a unit of time follows a Poisson process with mean λ. Suppose that λ = 9 for a particular image.
a. Find and interpret the mean of x.
b. Find the standard deviation of x.
c. The signal-to-noise ratio (SNR) for a penumbrol image is defined as SNR = μ/σ, where μ and s are the mean and standard deviation, respectively, of the noise process. Find the SNR for x.