answer question dii

PHYS10471 1. An experimental low-energy lightbulb is manufactured. When powered it is found that each bulb draws a current I with a probability density function equal to f (1) = Tax 1 - (Tomx) for 0 S IS Imax otherwise, where C is a constant. a) Show that C = 4/Imax [3 marks] b) Derive the cumulative distribution function for I. 4 marks c) The effective impedance of a bulb can be computed from Z = V/I. What is the expectation value of the impedance, (Z), for the bulbs in terms of V and Imax? [4 marks] d) For a particular batch of bulbs Imax = 30 mA. In order to meet regulations, the manufacturer recycles bulbs that draw a current greater than 20 mA. i) What fraction of bulbs are recycled in this way? [3 marks] ii) Show that the remaining bulbs have an expectation value (1) = 12.6 mA. [4 marks]