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Chapter 5: Q 19. (page 247)

Two random variables, X and Y, have standard deviations 2.4 and 3.6, respectively. Which one is more likely to take a value close to its mean? Explain your answer.

Short Answer

Expert verified

X is more likely to take a value close to its mean.

Step by step solution

01

Step 1. Given information.

The given statement is:

Two random variables, Xand Y, have standard deviations of 2.4 and 3.6, respectively.

02

Step 2. Determine the value close to its mean.

For any two random variables, the one with a lower standard deviation than the other's mean will take a value near to that of the other.

The random variable X has a lower mean than the random variable Y's standard deviation.

Because random variable X has a lower standard deviation than random variableY, it is more likely to take a value nearer to the mean.

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Most popular questions from this chapter

An experiment has 40 possible outcomes, all equally likely. An event can occur in 25 ways. The probability that the event is .

In each of Exercises 5.167-5.172, we have provided the number of trials and success probability for Bernoulli trials. Let X denote the total number of successes. Determine the required probabilities by using

(a) the binomial probability formula, Formula 5.4 on page 236. Round your probability answers to three decimal places.

(b) Table VII in Appendix A. Compare your answer here to that in part (a).

n=4,p=0.3,P(X=2)

In Exercises 5.16-5.26, express your probability answers as a decimal rounded to three places.

Coin Tossing. A balanced dime is tossed three times. The possible outcomes can be represented as follows.

Here, for example. HHT means that the first two tosses come up heads and the third tails. Find the probability that

(a) exactly two of the three tosses come up heads.

(b) the last two tosses come up tails.

(c) all three tosses come up the same.

(d) the second toss comes up heads.

What is the relationship between Bernoulli trials and the binomial distribution?

In each of Exercises 5.167-5.172, we have provided the number of trials and success probability for Bernoulli trials. LetX denote the total number of successes. Determine the required probabilities by using

(a) the binomial probability formula, Formula 5.4 on page 236. Round your probability answers to three decimal places.

(b) TableVII in AppendixA. Compare your answer here to that in part (a).

n=5,p=35,P(X=4)
See all solutions

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