A cubic die is biased, so that for each integer n, 1 ≤n ≤6, the probability of the event {n} is p({n}) = 2p if n=3 or n=4 and p({n}) = p, otherwise. a) What is the expected number of times the die comes up 6, when it is rolled 32 times? b) What is the expected number of times the die must be rolled until the first 6 comes up?

A cubic die is biased, so that for each integer n, 1 ≤n ≤6, the probability of the event {n} is p({n}) = 2p if n=3 or n=4 and p({n}) = p, otherwise. a) What is the expected number of times the die comes up 6, when it is rolled 32 times? b) What is the expected number of times the die must be rolled until the first 6 comes up?

A First Course in Probability (10th Edition)

10th Edition

ISBN:9780134753119

Author:Sheldon Ross

Publisher:Sheldon Ross

Chapter1: Combinatorial Analysis

Section: Chapter Questions

Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...

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