At the 10-years celebration of Alsion the students want to offer a game. The gam

Question

At the 10-years celebration of Alsion the students want to offer a game. The game consists of a 8-segment price wheel, where 5 field are "1", 3 fields are "2". The wheel is turned 3 times per game. The total value is disbursed in DKK. The random parameter X represents the disbursement per game. Find the probability distribution and the expected value of X. Calculate the standard deviation of X. Thomas suggests to improve the setup: "We should have two fields with "0", four fields with "1" and only two fields with "2". That will decrease the disbursement per game by at least 1 DKK. If we take a stake of 4 DKK we will make more money." Is he right? Comment also on the standard deviation change.

Explanation / Answer

a)

E[X] = 3*0.2441 + 4*0.4395 + 5*0.2627 + 6*0.0527 = 4.12

b) s = (3-4.12)2*0.244141 + (4-4.12)2*0.439453 + (5-4.12)2*0.263672 + (6-4.12)2*0.052734 = 0.703149

c)

E(X) = 3

The disbursement per game has decreased by atleast 1DKK. Since the probability for 4 DKK is lesser , there will be more payout.

The standard deviation is 1.5

X 3 4 5 6 P(X) 0.244141 0.439453 0.263672 0.052734

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