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Inequality 1 + x ≤ e holds for all real numbers. Suppose you have an number of times one must roll this die before we obtain a specific result of geometric distributions, that, in expectation, we will have to roll this d inequality above to determine the number m of die rolls necessary such the m rolls is at least 1 - for some constant c. ne m = n² m = n m = log n

Inequality 1 + x ≤ e holds for all real numbers. Suppose you have an number of times one must roll this die before we obtain a specific result of geometric distributions, that, in expectation, we will have to roll this d inequality above to determine the number m of die rolls necessary such the m rolls is at least 1 - for some constant c. ne m = n² m = n m = log n

Algebra & Trigonometry with Analytic Geometry
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter1: Fundamental Concepts Of Algebra
Section1.1: Real Numbers
Problem 25E
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Inequality 1+ x < e holds for all real numbers. Suppose you have an n-sided die with distinct faces. Let X be the number of times one must roll this die before we obtain a specific result 1 <r <n. We know from the properties of geometric distributions, that, in expectation, we will have to roll this die n times before we obtain r. Use the inequality above to determine the number m of die rolls necessary such that the probability of rolling r in any of the m rolls is at least 1 - for some constant c. n° = n? т — т — п m = log n m = n log n
Transcribed Image Text:Inequality 1+ x < e holds for all real numbers. Suppose you have an n-sided die with distinct faces. Let X be the number of times one must roll this die before we obtain a specific result 1 <r <n. We know from the properties of geometric distributions, that, in expectation, we will have to roll this die n times before we obtain r. Use the inequality above to determine the number m of die rolls necessary such that the probability of rolling r in any of the m rolls is at least 1 - for some constant c. n° = n? т — т — п m = log n m = n log n
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