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5. How does the equilibrium of the penalty kicks game (analyzed by Palacios-Huerta in his article)...

5. How does the equilibrium of the penalty kicks game (analyzed by Palacios-Huerta in his article) change if the goal-keeper improves her skills at saving penalty kicks kicked to the natural side of the kicker? Give a numerical example before and after improving her skills.

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Obtain the probability that all kicks are successful. That is, to find P(X -15) It is given that the random variable X is defined as number of penalty kicks by professional soccer players. Here, number of penalty kicks (n) is 15 and the probability of penalty kicks that are successful is 0.85. That is, the probability of success(p) is 0.85. Here, the random variable X follows the binomial probability distribution The binomial probability distribution formula is, n-x Substitute x-15, n 15, and p 0.85 15 15 15-15 P(X 15)(0.85) (1-0.85) -(D(085)5 (0.is) ((0.0874) (0) 0.0874 Thus, the probability that all kicks are successful is 0.0874

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