# Question: The following are some applications of the Markov inequality of

The following are some applications of the Markov inequality of Exercise 4.29:

(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.

(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.

## Answer to relevant Questions

A study of the nutritional value of a certain kind of bread shows that the amount of thiamine ( vitamin B1) in a slice may be looked upon as a random variable with µ = 0.260 milligram and s = 0.005 milligram. According to ...The length of certain bricks is a random variable with a mean of 8 inches and a standard deviation of 0.1 inch, and the thickness of the mortar between two bricks is a random variable with a mean of 0.5 inch and a standard ...In the proof of Theorem 5.2 we determined the quantity E[X(X – 1)], called the second factorial moment. In general, the rth factorial moment of X is given by µ'(r) = E[ X(X – 1)(X – 2) · . . . · (X – r + ...Prove Theorem 5.6 by first determining E(X) and E[X(X + 1)]. Theorem 5.6 The mean and the variance of the negative binomial distribution are µ = k/θ and σ2 = k/θ(1/θ – 1) Show that if we let θ = M/N in Theorem 5.7, the mean and the variance of the hypergeometric distribution can be written as µ = nθ and σ2 = nθ(1– θ) ∙ N – n / N – 1 . How do these results tie in with the ...Post your question