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Unformatted text preview: X n =3 ‡ z 2 · n2 = z 2 ∞ X n =1 ‡ z 2 · n = z 2 ± z 2 1z 2 ¶ = z 3 2z (3) To get the range and the probabilities, let’s just multiply it out: G X ( z ) = 1 z ± 1 3 z + 2 3 ¶ 4 = 1 z " ± 1 3 z ¶ 4 + 4 ± 1 3 z ¶ 3 ± 2 3 ¶ + 6 ± 1 3 z ¶ 2 ± 2 3 ¶ 2 + 4 ± 1 3 z ¶± 2 3 ¶ 3 + ± 2 3 ¶ 4 # = 1 81 z 3 + 8 81 z 2 + 24 81 z + 32 81 + 16 81 z1 We can now read the information oﬀ the function. The range is {1 , , 1 , 2 , 3 } and the mass function is: P [ X =1] = 16 81 P [ X = 0] = 32 81 P [ X = 1] = 24 81 P [ X = 2] = 8 81 P [ X = 3] = 1 81 Last compiled at 9:28 P.M. on July 12, 2011...
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This note was uploaded on 07/26/2011 for the course MATH 530 taught by Professor Warren during the Summer '10 term at Ohio State.
 Summer '10
 WARREN
 Probability

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