Question

Solve the two-person zero-sum game having the following payoff matrix for player A

  Player B
B1 B2 B3 B4 B5
Player A A1 3 4 5 –2 3
A2 1 6 –3 3 7
14 Feb 2023
Answer :
Word Count : 268

To solve this two-person zero-sum game, we can use the minimax theorem which states that in a zero-sum game, the player's optimal strategy is to minimize their maximum loss.

The given payoff matrix for player A is:

___ _________ _______ ________ ________ _____ _______ ________ ______ ___.
____ _________ ________ __________ ____ __________ _________ _____.
____ ______ _______ __________ ___ ______ ___ _____ ________ __________.
___ __________ _________ ______ __________ __________ ______ ___ ________ ___.
____ __________ __________ ________ ____ ________ ________.
_____ _____ _________ ________ ______ _____ __________ ____ ___.
________ ____ _________ ______ ______ ________.
______ ___ ________ _________ ____ __________ ___.
_______ ____ _____ ________ _________.
_____ ___ ________ _______ ______ _________ ____ _________ _______ __________ __________.
_________ _______ ___ ______ _________ ______ ______ ____ ___ ______ _______.
_______ ________ _________ _____ _____ ______ ___.
_________ _______ ____ ________ _____ _____ _______.
_____ ________ _____ _________ ____.
_________ ____ _______ ______ ___ _____ ___ _________ ______ ______ _______.
_____ __________ _______ ______ ______ ____ __________.
___ _____ ___ _______ ___ __________ ________ ________ ________ ___ ___.
______ _________ _________ _____ _____ __________.
__________ _____ _____ ___ _______ ___ _______ ________ ______ _________.
______ _________ _______ _____ ___ _____ __________ _____.
__________ __________ ______ _________ ____ __________ _____ _____ _________ ________ __________.
___ _______ ________ ___ ________ _______ _______ _______.
________ ______ ____ _____ ________ __________ _________.
_______ ___ ____ ___ _________ ________ ________.
_________ ______ ________ _______ _______ __________ ___ _______ _________ ______ __________.
_________ ________ ______ ___ ________.
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Related Questions

The failure density function of a random variable T is given by
f(t) = left{egin{matrix} 0.011e^{-0.01t}, & tgeq 0 \ 0, & otherwise end{matrix}ight.
Calculate, the
i) reliability of the component. 
ii) reliability of the component for a 100 hour mission time. 
iii) mean time to failure (MTTF). 
iv) median of the random variable T. 
v) life of the component, if the reliability of 0.96 is desired. 

The system shown below is made up of ten components. Components 3, 4 and 5 are not identical and at least one component of this group must be available for system success. Components 8, 9 and 10 are identical and for this particular group it is necessary that two out of the three components functions

Image ignouassignments-ignouacademy-com--p-matrix-17108

  Player B
B1 B2 B3
What is the system reliability if R1 = R 3 = R 5 = R 7 = R 9 = 0.85 and
R 2 = R 4 = R 6 = R 8 = R10 = 0.95

State whether the following statements are True or False. Give reason in support of your answer. 
a) If the average number of defects in an item is 4, the upper control limit of the c-chart will be 12.
b) The specification limits and natural tolerance limits are same in statistical quality control.
c) If the probability of making a decision about acceptance or rejection of a lot on the first sample is 0.80 and the sizes of the first and second samples are 10 and 15, respectively, then
the average sample number for the double sampling plan will be 25.
d) Two independent components of a system are connected in series configuration. If the reliabilities of these components are 0.1 and 0.30, respectively then the reliability of the system will be 0.65.
e) A point in the pictorial representation of a decision tree having states of nature as immediate sub-branches is known as decision point. 

 

A shirt manufacturing company supplies shirts in lots of size 250 to the buyer. A single sampling plan with n = 20 and c = 1 is being used for the lot inspection. The company and the buyer decide that AQL = 0.04 and LTPD = 0.10. If there are 15  defective in each lot, compute the
i) probability of accepting the lot. 
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A small electronic device is designed to emit a timing signal of 200 milliseconds (ms) duration. In the production of this device, 10 subgroups of four units are taken at periodic intervals and tested. The results are shown in the following table: 

Subgroup Number Duration of Automatic Signal (in ms)
a b c d
1 195 201 194 201
2 204 190 199 195
3 195 197 205 201
4 211 198 193 180
5 204 193 197 200
6 200 202 195 200
7 196 198 197 196
8 201 197 206 207
9 200 202 204 192
10 203 201 209 192

 i) Estimate the process mean and standard deviation. 
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iii) By plotting the charts on graph paper, determine that the process is stable or not with respect to the process mean and process variability. If necessary, compute revised control limits

Solve the two-person zero-sum game having the following payoff matrix for player A

  Player B
B1 B2 B3 B4 B5
Player A A1 3 4 5 –2 3
A2 1 6 –3 3 7

To monitor the manufacturing process of mobile phones, a quality controller randomly selected 100 mobile phones from the production line, each day over 15 days. The mobile phones were inspected for defectives and the number of defective mobile phones found each day was recorded. The data are given below:

Subgroup Number Number of Mobile Phones Inspected Number of Defective Mobile Phones
1 100 3
2 100 6
3 100 4
4 100 6
5 100 20
6 100 2
7 100 6
8 100 7
9 100 3
10 100 0
11 100 6
12 100 15
13 100 5
14 100 7
15 100 6

 i) Determine the trial centre line and control limits for the fraction defective using the above data. 

ii) Contract the control chart on graph paper and determine that the process is stable or not. If there is any out-of-control point, determine the revised centre line and control limits.

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