3. (4 pts) Let Y1, Y2, Y3, - - . be (not necessarily independent) non-negative random vari- ables, such that E [Yi] s 2". Define a new random variable Z = 2:1 Y,- . Despite neither knowing the distribution of the Yg's nor how they depend on each other, show that you can use Markov's inequality to nd out that: P(2210) 50.1. Possible scenario: Y; = radiation exposure of a Mars settlement on week 1'. Each week, additional shielding is built and Y; goes down in expectation. However. there is a complex dependence between progress at different times. Despite this, if in-expectation decay is fast. the probability of large total radiation exposure remains low