4. A space probe encounters a planet capable of sustaining lifeon average every 3.4 lightyears. (Recall that a lightyear is ameasure of distance, not time.)
a) Let L be the number of life-sustaining planets that the probeencounters in 10 lightyears. What are the distribution,parameter(s), and support of L?
b) What is the probability that the probe encounters at least 2life-sustaining planets in 10 lightyears?
c) The probe has just encountered a life-sustaining planet. Whatis the probability that it takes more than 4 lightyears toencounter the next life-sustaining planet? What distribution andparameter(s) are you using?
d) Suppose the probe has not encountered a life-sustainingplanet for 2.5 lightyears. Knowing this, what is the probabilitythat it will take at most 8 lightyears to detect the nextlife-sustaining planet?
e) The probe has encountered 10 life-sustaining planets in thelast 25 lightyears. What is the probability that there are 3life-sustaining planets in the first 5 lightyears of this25-lightyear span?
