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Probability bounds using Chebychev's inequality

Many people believe that the daily charge of a price of a company's stock on the stock market is a random variable with mean 0 and variance {see attachment}. That is, if Yn represents the price of the stock on the n-th day, then (see equation in attachment( where X1,X2,..., are independent and identically distributed random variables with mean 0 and variance {see attachment}.

Suppose that the stock's price today is 100. If the variance =1, what can you say about that probability that the stock's price will exceed 105 after 10 days, without using the Central Limit Theorem?

*Please see attachment for functions


Solution Summary

In this solution, Chebychev's inequality is used to find bounds on the probability of a function of a set of random variables.