Probability Casino Question

[picrazy1010]

Your local casino acquires some new slot machines, which the manufacturer says gives the player a 1% chance of winning. However your friend at the manufacturing company claims to have secretly tampered with one of the slot machines, so that the player actually has a 10% chance of winning on that machine. You decide to trust your friend with your life’s savings and play at that machine 1,000 times. Assume that the 1,000 play outcomes can be represented by independent, identically distributed Bernoulli random variables with unknown but fixed parameter p, where p = 0.01 or p = 0.1. What integer is closest to B/5, where B is the decision boundary, in terms of the number of times out of 1,000 that you win, for the maximum likelihood estimator of the parameter p?

 

[mmm4444bot]

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