A manufacturer produces diodes. It is estimated that 0.25% of the diodes are defective. A diode being defective is independent on the condition of the other diodes. The manufacturer can do the following tests to determine which diodes are defective. To test each diode individually costs 6 cents per diode. To test a group of n diodes costs a total of 5 + n cents. The company is considering the following strategy to test the diodes. First, test a group of n diodes and assume that n is an even number. If the group doesn't clear, split the group into 2 halves. Test the first half. If it clears, test all from the second half. If the first half doesn't clear, test all from the first half, then test the second half. If the second half doesn't clear, test all in the second half. Let T be the average cost per diode. (a) What would be the sample space for T? (That is, what would be all possible values for T?) (b) Find the probability distribution for T. (You can write up a probability mass function table.) (c) Find the expected value of T, E(T). (d) Explain how you will find the value of n that will give the smallest expected cost per diode. (no actual calculations).