Question - Six Degrees of Kevin Bacon The actor Kevin Bacon has been in so many movies that almost everyone in Hollywood can be connected to him within six degrees. Let n 5 1,326,359, the number of actors linked to Kevin Bacon. The probability distribution for the Bacon Number of a randomly selected Hollywood personality is given in the following table.
|
x
|
p(x)
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x
|
p(x)
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x
|
p(x)
|
|
0
|
1/n
|
1
|
2511/n
|
2
|
262,544/n
|
|
3
|
839,562/n
|
4
|
204,764/n
|
5
|
15,344/n
|
|
6
|
1397/n
|
7
|
204/n
|
8
|
32/n
|
a. Find the mean, variance, and standard deviation for the Bacon Number.
b. Find P(X ≥ μ - σ).
c. The number of movies, Y, in which a Hollywood personality has appeared is related to the Bacon Number by the formula Y = 2X + 5. Find the mean, variance, and standard deviation of the number of movies in which a Hollywood personality has appeared.