# Normal approximation to binomial, central limit theorem- gambling

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1. (A Gambling Example). It costs one dollar to play a certain slot machine in Las Vegas. The machine is set by the house to pay two dollars with probability .45 (and to pay nothing with probability .55). Let Xi be the house's net winnings on the ith play of the machine. Then Sn=?in=1 Xi is the house's winnings after n plays of the machine. Assuming that successive plays are independent, find

a) E(Sn)

b) Var(Sn)

c) The approximate probability that after 10,000 plays of the machine the house's winnings are between 800 and 1100 dollars.

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The expert examines the normal approximation binomial and the central limit theorem for gambling.

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