For this problem, my task is simple. I have to be able to "summarize what key concepts are being explained in the example. I have to summarize what the problem is explaining and the bottom-line concepts described in the problem."

Can you help me summarize what this problem is stating and be able to explain it in basic English? Thank you.

Images displayed on computer screens consist of thousands of small regions called picture elements, or pixels for short. The intensity of the electron beam focused at a given point (x0, yo) on a flat screen is usually described by two in- dependent normal random variables x and y, with means x0 and yo, respectively. That is, we represent the intensity of the beam by a joint density function of two independent random variables. For example, Figure 5.14 shows a graph of the joint density function describing an electron beam focused on the point (x0, yo) = (30, 50). The standard deviations of the two normal distributions are 0'1 = .2 and cry = .2. Because x and y are independent, we can write the joint density as the product x, 3') = 1300130?) _ 1 Adz. 1 4&2 mm Wm - 1 e-%[("T:\")z+(%zl Zara'xa), Figure 5.I4 Joint density function near the point (ero) = (30-50) The volume under this density that sits over a given region B in the xy plane describes the proportion of time that the electron beam spends in region B. Although the joint density can be used to nd the probability associated with any set B of points near (30, 50) on the screen, the probability of some sets can be found in an easier way. For example, if we want to nd the proportion of time that the beam spends in the region where x