An executive must decide between two competing techniques to complete a given task. Technique A will work only 15% of the time, but only costs $300. Technique B will work 55% of the time and costs $5000. The executive must balance time versus cost, so he decides on the following rule: Try technique A for a set number of times, k. If it doesn't work, switch to technique B and keep trying that until success occurs. He must therefore find the expected number of attempts and the expected cost for various values of the variable k.

a. Give a probability mass function for the number of attempts if k=3.

b. Write, but do not evaluate, the formula for expected number of attempts with k=3

c. Give a probability mass function for the cost of success if k=2.

d. Write, but do not evaluate, the formula for the expected cost of success for k=2.

e. (5 points extra credit) Evaluate the formulas you found in b and d.