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2 answers:
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Answer:
Explained below.
Step-by-step explanation:
The random variable <em>X</em> is defined as the number of stars in a given volume of space.
The probability mass function of <em>X</em> is:
(7)
Compute the probability of exactly two stars in 16 cubic light-years as follows:
(8)
Compute the probability of three or more stars in 16 cubic light-years as follows:
(9)
In 16 cubic light years there is only 1 star.
Then in 1 cubic light years there will be, (1/16) stars.
Then in 4 cubic light years there will be, 4 × (1/16) = (1/4) stars.
(10)
In 16 cubic light years there is only 1 star.
Then in 1 cubic light years there will be, (1/16) stars.
Then in <em>t</em> cubic light years there will be, [<em>t</em> × (1/16)] stars.