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Unformatted text preview: X n =3 â€¡ z 2 Â· n2 = z 2 âˆž X n =1 â€¡ z 2 Â· n = z 2 Â± z 2 1z 2 Â¶ = z 3 2z (3) To get the range and the probabilities, letâ€™s just multiply it out: G X ( z ) = 1 z Â± 1 3 z + 2 3 Â¶ 4 = 1 z " Â± 1 3 z Â¶ 4 + 4 Â± 1 3 z Â¶ 3 Â± 2 3 Â¶ + 6 Â± 1 3 z Â¶ 2 Â± 2 3 Â¶ 2 + 4 Â± 1 3 z Â¶Â± 2 3 Â¶ 3 + Â± 2 3 Â¶ 4 # = 1 81 z 3 + 8 81 z 2 + 24 81 z + 32 81 + 16 81 z1 We can now read the information oï¬€ 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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 Summer '10
 WARREN
 Probability, Probability theory, Probabilitygenerating function, Generating function, Gx, mass function

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