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Suppose we have 30 exponential random variables with mean 10. Find the probability that the sum...

Suppose we have 30 exponential random variables with mean 10. Find the probability that the sum of the random variables is larger than 12. Find also the probability that the average value of all those 30 random variables is larger than 12. Then find the probability that one of the random variables is larger than 12. Compare these probabilities.

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Given the RV . According to CLT, is distributed approximately as

. The probability

According to CLT, is distributed approximately as

. The probability

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