12 diamonds are ranked from 1 to 12 according to quality. Three diamonds are sel

Question

12 diamonds are ranked from 1 to 12 according to quality. Three diamonds are selected at random without replacement from the 12. Let X equal the sum of the ranks of the 3 diamonds.
a.) How many points are in the sample space?
- I have s = {X = 6, X = 7, X = 8, ... X = 33}; therefore there are 27 sample spaces.
b.) Describe a one point in the sample space.
- I have X = 6, the sum of the three diamonds equals six.
c.) Find P (X = 3).
- I have this as 0/27 = 0.
d.) If f(x) is the probability function of X find f(10).
- I think this would be P(X = 10). I wrote it up and found it to be 4/27, I don't know if there is a shortcut way to do it
e.) If F(X) is the distribution function of X, find F(10).
f.) Use the central limit theorem to approximate F(10) and compare this approximation with the exact value found in part e.

-Having trouble with d, e, f.
Thanks

Explanation / Answer

(d) If f(x) is the probability function of X, find f(10). Four combinations {(1,3,6), ?1,4.5?, (1,2,7), (2,3,4)} lead to the sum of 10 (X=10). So, f(10)=4/220=1/55. (e) Let F(x) is the distribution function of X, find F(10). F(10)=P(x

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