A fair die is rolled whose six sides are labeled 1, 2, 2, 3, 3, 3. Let D be the number that comes up. (a) Find the z-transform Db (z), defined to be E[z^D]. (b) Let D1, D2, D3, D4 be four independent copies of D (that is, the results of four rolls of the die), and let S = D1 + D2 + D3 + D4. Find the z-transform Sb(z). (Don’t expand.) (c) Wolfram Alpha told me that when you expand the answer to (b), you should get z^4/1296 + z^5/162 + z^6/36 + 13z^7/162 + 107z^8/648 + 13z^9/54 + z^10/4 + z^11/6 + z^12/16. Using this information, what is Pr[S ≥ 10]?

A fair die is rolled whose six sides are labeled 1, 2, 2, 3, 3, 3. Let D be the number that comes up. (a) Find the z-transform Db (z), defined to be E[z^D]. (b) Let D1, D2, D3, D4 be four independent copies of D (that is, the results of four rolls of the die), and let S = D1 + D2 + D3 + D4. Find the z-transform Sb(z). (Don’t expand.) (c) Wolfram Alpha told me that when you expand the answer to (b), you should get z^4/1296 + z^5/162 + z^6/36 + 13z^7/162 + 107z^8/648 + 13z^9/54 + z^10/4 + z^11/6 + z^12/16. Using this information, what is Pr[S ≥ 10]?

Elementary Linear Algebra (MindTap Course List)

8th Edition

ISBN:9781305658004

Author:Ron Larson

Publisher:Ron Larson

Chapter5: Inner Product Spaces

Section5.5: Applications Of Inner Product Spaces

Problem 91E

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