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The following are some applications of the Markov inequality of Exercise 29:

(a) The scores that high school juniors get on the verbal part of the PSAT/NMSQT test may be looked upon as values of a random variable with the mean μ = 41. Find an upper bound to the probability that one of the students will get a score of 65 or more.

(b) The weight of certain animals may be looked upon as a random variable with a mean of 212 grams. If none of the animals weighs less than 165 grams, find an upper bound to the probability that such an animal will weigh at least 250 grams

Exercise 29

Show that if X is a random variable with the mean μ for which f(x) = 0 for x

This inequality is called Markov's inequality, and we have given it here mainly because it leads to a relatively simple alternative proof of Chebyshev's theorem.

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