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In a game played with dice, Ali or Bob is selected with a probability of 5 and , respectively. The dice are fair and four-sided with the values of 1, 2, 3 and 4. If selected, Ali will roll a die until he obtains the second value of 4 and the number of rolls required is recorded. If selected, Bob will roll two dice and the sum of the obtained values is recorded. Let X denote the recorded outcome of the game. Find P(X ≤ 3). Show that the moment generating function (mgf) for X is 2 et 3³ (4-130²) + 5 3et 40 (i) (ii) (iii) M (t) = 4 x=1 Hence, using part (ii), find the mean of X. 2 t < ln 4

In a game played with dice, Ali or Bob is selected with a probability of 5 and , respectively. The dice are fair and four-sided with the values of 1, 2, 3 and 4. If selected, Ali will roll a die until he obtains the second value of 4 and the number of rolls required is recorded. If selected, Bob will roll two dice and the sum of the obtained values is recorded. Let X denote the recorded outcome of the game. Find P(X ≤ 3). Show that the moment generating function (mgf) for X is 2 et 3³ (4-130²) + 5 3et 40 (i) (ii) (iii) M (t) = 4 x=1 Hence, using part (ii), find the mean of X. 2 t < ln 4

College Algebra
College Algebra
10th Edition
ISBN:9781337282291
Author:Ron Larson
Publisher:Ron Larson
Chapter8: Sequences, Series,and Probability
Section: Chapter Questions
Problem 41CT: On a game show, a contestant is given the digits 3, 4, and 5 to arrange in the proper order to form...
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and In a game played with dice, Ali or Bob is selected with a probability of respectively. The dice are fair and four-sided with the values of 1, 2, 3 and 4. If selected, Ali will roll a die until he obtains the second value of 4 and the number of rolls required is recorded. If selected, Bob will roll two dice and the sum of the obtained values is recorded. Let X denote the recorded outcome of the game. Find P(X ≤ 3). Show that the moment generating function (mgf) for X is 2 et M(C) = ² ( = = 12 ) ² + + (20²)² = + < In (1) 1 4 Σ ptx 4 3et 40 (i) (ii) (iii) x=1 315 Hence, using part (ii), find the mean of X.
Transcribed Image Text:and In a game played with dice, Ali or Bob is selected with a probability of respectively. The dice are fair and four-sided with the values of 1, 2, 3 and 4. If selected, Ali will roll a die until he obtains the second value of 4 and the number of rolls required is recorded. If selected, Bob will roll two dice and the sum of the obtained values is recorded. Let X denote the recorded outcome of the game. Find P(X ≤ 3). Show that the moment generating function (mgf) for X is 2 et M(C) = ² ( = = 12 ) ² + + (20²)² = + < In (1) 1 4 Σ ptx 4 3et 40 (i) (ii) (iii) x=1 315 Hence, using part (ii), find the mean of X.
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