Assume you have a typical fair 6-sided die. That is to say, it has sides 1, 2, 3, 4, 5, 6 and each side has probability of 1/6 of occurring. You are to roll the die twice, and record the maximum, M, of the two 6 rolls. If you roll a 2 and a 3 (or a 3 and a 2), then M = 3. If you roll a 4 and a 4, then M = 4. The rolls are independent of each other. a. Derive the probability table for M. That is to say P(M = m) for m=1,2,3,4,5,6. b. Find the expected value of M, E(M)
Assume you have a typical fair 6-sided die. That is to say, it has sides 1, 2, 3, 4, 5, 6 and each side has probability of 1/6 of occurring. You are to roll the die twice, and record the maximum, M, of the two 6 rolls. If you roll a 2 and a 3 (or a 3 and a 2), then M = 3. If you roll a 4 and a 4, then M = 4. The rolls are independent of each other. a. Derive the probability table for M. That is to say P(M = m) for m=1,2,3,4,5,6. b. Find the expected value of M, E(M)
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter10: Sequences, Series, And Probability
Section10.8: Probability
Problem 6E
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Assume you have a typical fair 6-sided die. That is to say, it has sides 1, 2, 3, 4, 5, 6 and each side has probability of 1/6 of occurring. You are to roll the die twice, and record the maximum, M, of the two 6 rolls. If you roll a 2 and a 3 (or a 3 and a 2), then M = 3. If you roll a 4 and a 4, then M = 4. The rolls are independent of each other.
a. Derive the probability table for M. That is to say P(M = m) for m=1,2,3,4,5,6.
b. Find the
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