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4. A space probe encounters a planet capable of sustaining life on average every 3.4 lightyears....

4. A space probe encounters a planet capable of sustaining life on average every 3.4 lightyears. (Recall that a lightyear is a measure of distance, not time.)

a) Let L be the number of life-sustaining planets that the probe encounters in 10 lightyears. What are the distribution, parameter(s), and support of L?

b) What is the probability that the probe encounters at least 2 life-sustaining planets in 10 lightyears?

c) The probe has just encountered a life-sustaining planet. What is the probability that it takes more than 4 lightyears to encounter the next life-sustaining planet? What distribution and parameter(s) are you using?

d) Suppose the probe has not encountered a life-sustaining planet for 2.5 lightyears. Knowing this, what is the probability that it will take at most 8 lightyears to detect the next life-sustaining planet?

e) The probe has encountered 10 life-sustaining planets in the last 25 lightyears. What is the probability that there are 3 life-sustaining planets in the first 5 lightyears of this 25-lightyear span?

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milcah answered 1 year ago
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