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A quality control engineer wants to estimate the expected fraction of original voltage that is lost after an hour of continuously running a mechanical rabbit
A quality control engineer wants to estimate the expected fraction of original voltage that is lost after an hour of continuously running a mechanical rabbit for randomly chosen batteries her company produces. Suppose that the true fractional voltage loss for randomly chosen batteries is distributed according to some unknown random variable B. She knows for sure that [B] 2 0.01. To do this she will run n independent trials and measure the fractional loss X1- of the original voltag_e at the end of hour for batteries 2' = 17 . . . ,n, compute the sum X = 221:1 Xi, and output the average loss, X = X as her estimate of 1E[B]. Using only the version of the Chernoff bound that we are have given in CSE 312,_how many independent trials n will she need to guarantee that with probability 99%, the average fractional loss X that she measures is at most twice the true expected loss fraction iE[B]
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