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A fair die is rolled whose sides are labeled 2, 3, 3, 3, 5, 5. Let D be the number that comes up. (a) Find the z-transform Ô(z) of D, defined to be E[zº]. (b) Let D₁, D2, D3 be three independent copies of D, and let S = D₁ + D2 + D3. Find the z-transform S(z) by using your answer to (a). (c) Your answer to (b) should expand out to the polynomial 215 z13 z12 z11 z10 11z⁹ 28 27 + + + + + 6 27 6 18 4 + + + 72 8 24 216 (I asked Mathematica.) Using this information, what is the probability Pr[S ≥ 12]?

A fair die is rolled whose sides are labeled 2, 3, 3, 3, 5, 5. Let D be the number that comes up. (a) Find the z-transform Ô(z) of D, defined to be E[zº]. (b) Let D₁, D2, D3 be three independent copies of D, and let S = D₁ + D2 + D3. Find the z-transform S(z) by using your answer to (a). (c) Your answer to (b) should expand out to the polynomial 215 z13 z12 z11 z10 11z⁹ 28 27 + + + + + 6 27 6 18 4 + + + 72 8 24 216 (I asked Mathematica.) Using this information, what is the probability Pr[S ≥ 12]?

Trigonometry (MindTap Course List)
Trigonometry (MindTap Course List)
10th Edition
ISBN:9781337278461
Author:Ron Larson
Publisher:Ron Larson
Chapter6: Topics In Analytic Geometry
Section6.4: Hyperbolas
Problem 5ECP: Repeat Example 5 when microphone A receives the sound 4 seconds before microphone B.
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1. A fair die is rolled whose sides are labeled 2, 3, 3, 3, 5, 5. Let D be the number that comes up. (a) Find the z-transform D(z) of D, defined to be E[₂¹]. (b) Let D₁, D2, D3 be three independent copies of D, and let S = D₁ + D2 + D3. Find the z-transform S(z) by using your answer to (a). (c) Your answer to (b) should expand out to the polynomial 215 z13 212 211 z10 112⁹ 28 + + + + + 27 6 18 4 6 26 + + + 72 8 24 216* (I asked Mathematica.) Using this information, what is the probability Pr[S ≥ 12]?
Transcribed Image Text:1. A fair die is rolled whose sides are labeled 2, 3, 3, 3, 5, 5. Let D be the number that comes up. (a) Find the z-transform D(z) of D, defined to be E[₂¹]. (b) Let D₁, D2, D3 be three independent copies of D, and let S = D₁ + D2 + D3. Find the z-transform S(z) by using your answer to (a). (c) Your answer to (b) should expand out to the polynomial 215 z13 212 211 z10 112⁹ 28 + + + + + 27 6 18 4 6 26 + + + 72 8 24 216* (I asked Mathematica.) Using this information, what is the probability Pr[S ≥ 12]?
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