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Chapter 5: Q 5.132. (page 230)

In Exercise 5.129 - 5.132, We have provided the probability distributions of the random variables considered in Exercise 5.109 - 5.112 of section 5.4 For each exercise, do the following tasks.

Part (a) Find the mean of the random variable.

Part (b) Obtain the standard deviation of the random variable by using one of the formulas given in definition 5.10.

Short Answer

Expert verified

Part (a) 渭=7.08

Part (b)蟽鈮�1.1

Step by step solution

01

Part (a) Step 1. Given information. 

x578
P(X=x)0.200.320.48
02

Part (a) Step 2. A random variable's mean is;

渭=鈭�x路(X=x)渭=5脳0.20+7脳0.32+8脳0.48渭=7.08

03

Part (b) Step 1.The random variable's standard deviation:

We have subpart (a) 渭=7.08

x
P(X=x)
x2
x2P(X=x)
50.20255
70.324915.68
80.486430.72
Total

51.4

The standard deviation is defined as

鈭�x2P(X=x)-渭2蟽=51.4-7.082蟽=1.2736蟽=1.1285蟽鈮�1.1

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Most popular questions from this chapter

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

Occupations in Seoul. The population of Seoul was studied in an article by B. Lee and J. McDonald, "Determinants of Commuting Time and Distance for Seoul Residents: The Impact of Family Status on the Commuting of Women" (Urban Studies, Vol. 40, No. 7, pp. 1283-1302). The authors examined the different occupations for males and females in Seoul. The table at the top of the next page is a frequency distribution of occupation type for males taking part in a survey. (Note: M = manufacturing, N = nonmanufacturing.)

If one of these males is selected at random, find the probability that his occupation is

(a) service.

(b) administrative.

(c) manufacturing.

(d) not manufacturing.

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=4,p=14,P(X=2)

What does it mean three events to be mutually exclusive.?

List the three requirements for repeated trials of an experiment to constitute Bernoulli trials.

Answer true or false to the following statement and justify your answer. If event A and event B are not mutually exclusive, neither are events A,B and C for every event C.
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