Alice walks into a post office with 2 clerks. both clerks are in the midst of serving

customers, but alice is next in line. the clerk on the left takes an expo(λ1) time to

serve a customer, and the clerk on the right takes an expo(λ2) time to serve a customer. let t be the amount of time alice has to wait until it is her turn.

(a) write down expressions for the mean and variance of t, in terms of double integrals

(which you do not need to evaluate).

(b) find the distribution, mean, and variance of t, without using calculus.

For this option, you will work individually. the pythagorean theorem can be used in many real-world scenarios. part 1 write your own real-world scenario where the pythagorean theorem can be applied to find a missing piece. you may choose to write a problem that is two- or three-dimensional in nature. be sure that you will be able to draw a diagram of your scenario. write out your problem and submit it for part 1. be sure to end your scenario with a question. part 2 draw a diagram of the scenario you created in part 1. you may draw by hand and scan and upload your drawing or create a computer-generated drawing for submission. be sure to label all parts and dimensions of the drawing. part 3 solve the question that you posed in part 1. show all of your steps in answering the question. for this option, you will need to submit all three parts for full credit—your real-world problem and question, the diagram that you created, and your work solving the problem, showing all steps. * note that your instructor is looking for your own original idea. while it is acceptable to use the internet for research and inspiration, academic integrity policies apply.