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Consider repeated rolling of a fair die, and assume that the different rolls are independent. For i = 1,2,3, 4, 5, denote by N, the minimum number of additional rolls needed for another distinct face (one of the remaining 6-i faces) to show up, after i distinct faces have shown up. Denote by N the minimum number of rolls needed for each of the six faces of the die to show up at least once. (a) Derive the pmf of Nj. Which common distribution is this (specify the name and the value(s) of the parameter(s))? (b) Write N as a suitable function of the N,'s and, based on this representation, determine EN and VN. Hint: In this exercise, you do not have to derive expectations and variances of common distributions-it suffices to look them up.

Consider repeated rolling of a fair die, and assume that the different rolls are independent. For i = 1,2,3, 4, 5, denote by N, the minimum number of additional rolls needed for another distinct face (one of the remaining 6-i faces) to show up, after i distinct faces have shown up. Denote by N the minimum number of rolls needed for each of the six faces of the die to show up at least once. (a) Derive the pmf of Nj. Which common distribution is this (specify the name and the value(s) of the parameter(s))? (b) Write N as a suitable function of the N,'s and, based on this representation, determine EN and VN. Hint: In this exercise, you do not have to derive expectations and variances of common distributions-it suffices to look them up.

Algebra & Trigonometry with Analytic Geometry
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter10: Sequences, Series, And Probability
Section: Chapter Questions
Problem 63RE
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Consider repeated rolling of a fair die, and assume that the different rolls are independent. For i 1,2, 3, 4, 5, denote by N, the minimum number of additional rolls needed for another distinct face (one of the remaining 6-i faces) to show up, after i distinct faces have shown up. Denote by N the minimum number of rolls needed for each of the six faces of the die to show up at least once. (a) Derive the pmf of N. Which common distribution is this (specify the name and the value(s) of the parameter(s))? (b) Write N as a suitable function of the N,'s and, based on this representation, determine EN and VN. Hint: In this exercise, you do not have to derive expectations and variances of common distributions-it suffices to look them up.
Transcribed Image Text:Consider repeated rolling of a fair die, and assume that the different rolls are independent. For i 1,2, 3, 4, 5, denote by N, the minimum number of additional rolls needed for another distinct face (one of the remaining 6-i faces) to show up, after i distinct faces have shown up. Denote by N the minimum number of rolls needed for each of the six faces of the die to show up at least once. (a) Derive the pmf of N. Which common distribution is this (specify the name and the value(s) of the parameter(s))? (b) Write N as a suitable function of the N,'s and, based on this representation, determine EN and VN. Hint: In this exercise, you do not have to derive expectations and variances of common distributions-it suffices to look them up.
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