The CSE Department of HKUST has a total of n light bulbs and m switches. We know that each light bulb is connected to at least one switch. By flipping a switch, the status of every light bulb connected to it will change (so if it was OFF it will be turned ON and vice versa). Assume Xi is the random variable that shows the status of the ith light
bulb. Xi = 0 means the ith light bulb is OFF and Xi = 1 means it is ON. Also, let Y be the random variable that denotes the number of light bulbs that are ON in the department, i.e., Y = Xi. Note that the initial status of every light bulb is arbitrary. Imagine you flip every switch with 50% probability. What is the expected value of Xi, where i = 1,2,···,n? Briefly explain why.