Noise in laser imaging. 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 l. Suppose that l = 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 = m>s, where m and s are the mean and standard deviation, respectively, of the noise process.

Find the SNR for x.