Question 2: Discrete Random Variables (15 points) 1. (5pts) When do you use a Binomial and when a Geometric random variable to model a statistical experiment? Explain briey. 2. (5pts) Suppose that 90% of all messages sent to us by aliens get lost in space and never reach earth. Further, suppose that the Goldstone Radio Telescope (GRT) in the Mojave Desert detects about 5% of all alien messages that reach earth in one year. Let W be the time in years until the GET detects an alien message for the rst time. If the events \"alien messages getting lost in space\" and \"alien messages being detect by the GET\" are independent, what is the probability P(W > 3)? 3. (5pts) Suppose that Elon Musk's vision of humanity becoming a Spacefaring species becomes reality. Spacefaring turns out to be an extremely dangerous business with only 12.5% of the spaceships reaching their destination. If spaceships succeed at reaching their destination independently of each other, how many spaceships does one have to send to a faraway colony to ensure that, on average (Le. in expectation), at least one spaceship reaches that colony