EBK STATISTICS FOR MANAGEMENT AND ECONO
EBK STATISTICS FOR MANAGEMENT AND ECONO
10th Edition
ISBN: 8220102958609
Author: KELLER
Publisher: YUZU
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Question
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Chapter 7.1, Problem 18E

(a)

To determine

Calculate the mean and variance.

(a)

Expert Solution
Check Mark

Explanation of Solution

The probability distribution of random variable X is shown below:

Table 1

X-2578
P(X)0.590.150.250.01

The mean value of the probability distribution of X is calculated as follows:

μ=E(X)=xP(x)=(2(0.59) + 5(0.15) + 7(0.25) + 8(0.01))=1.40

The mean value is 1.40.

The variance of the probability distribution of X is calculated as follows:

σ2=V(X)=(x-μ)2P(x)={(21.4)2(0.59)+(51.4)2(0.15)+(71.4)2(0.25)+(81.4)2(0.1)}=17.04

The variance is 17.04.

Economics Concept Introduction

Probability distribution: The probability distribution shows the probabilities of incidence of different likely outcomes in a test.

(b)

To determine

The probability distribution of Y.

(b)

Expert Solution
Check Mark

Explanation of Solution

The probability distribution of Y where Y is equal to 5X is shown in the below table:

X-2578
Y-10253540
P(Y)0.590.150.250.01

(c)

To determine

The mean and variance of Y.

(c)

Expert Solution
Check Mark

Explanation of Solution

The mean value of the probability distribution of Y is calculated as follows:

μ=E(Y)=yP(y)=(10(0.59) + 25(0.15) + 35(0.25) + 40(0.01))=7

The mean value is 7.

The variance of the probability distribution of Y is calculated as follows:

σ2=V(Y)=(y-μ)2P(y)={(107)2(0.59)+(257)2(0.15)+(357)2(0.25)+(407)2(0.1)}=426

The variance is 426.

(d)

To determine

The expected value and variance of Y.

(d)

Expert Solution
Check Mark

Explanation of Solution

The expected value of Y from Parameter X is calculated as follows:

E(Y)=E(5X)=5E(X) =5(1.4)=7

The expected value is 7.

The variance of Y from Parameter X is calculated as follows:

V(Y)=V(5X)=5V(X) =25(17.04) =426

The variance is 426.

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Chapter 7 Solutions

EBK STATISTICS FOR MANAGEMENT AND ECONO

Ch. 7.1 - Prob. 11ECh. 7.1 - Prob. 12ECh. 7.1 - Prob. 13ECh. 7.1 - Prob. 14ECh. 7.1 - Prob. 15ECh. 7.1 - Prob. 16ECh. 7.1 - Prob. 17ECh. 7.1 - Prob. 18ECh. 7.1 - Prob. 19ECh. 7.1 - Prob. 20ECh. 7.1 - Prob. 21ECh. 7.1 - Prob. 22ECh. 7.1 - Prob. 23ECh. 7.1 - Prob. 24ECh. 7.1 - Prob. 25ECh. 7.1 - Prob. 26ECh. 7.1 - Prob. 27ECh. 7.1 - Prob. 28ECh. 7.1 - Prob. 29ECh. 7.1 - Prob. 30ECh. 7.1 - Prob. 31ECh. 7.1 - Prob. 32ECh. 7.1 - Prob. 33ECh. 7.1 - Prob. 34ECh. 7.1 - Prob. 35ECh. 7.1 - Prob. 36ECh. 7.1 - Prob. 37ECh. 7.1 - Prob. 38ECh. 7.1 - Prob. 39ECh. 7.1 - Prob. 40ECh. 7.1 - Prob. 41ECh. 7.1 - Prob. 42ECh. 7.2 - Prob. 43ECh. 7.2 - Prob. 44ECh. 7.2 - Prob. 45ECh. 7.2 - Prob. 46ECh. 7.2 - Prob. 47ECh. 7.2 - Prob. 48ECh. 7.2 - Prob. 49ECh. 7.2 - Prob. 50ECh. 7.2 - Prob. 51ECh. 7.2 - Prob. 52ECh. 7.2 - Prob. 53ECh. 7.2 - Prob. 54ECh. 7.2 - Canadians who visit the United Sates often buy...Ch. 7.2 - Prob. 56ECh. 7.2 - Prob. 57ECh. 7.2 - Prob. 58ECh. 7.2 - Prob. 59ECh. 7.2 - Prob. 60ECh. 7.3 - Prob. 61ECh. 7.3 - Prob. 62ECh. 7.3 - Prob. 63ECh. 7.3 - Prob. 64ECh. 7.3 - Prob. 65ECh. 7.3 - Prob. 66ECh. 7.3 - Prob. 67ECh. 7.3 - Prob. 68ECh. 7.3 - Prob. 69ECh. 7.3 - Prob. 70ECh. 7.3 - Prob. 71ECh. 7.3 - Prob. 72ECh. 7.3 - Prob. 73ECh. 7.3 - Prob. 74ECh. 7.3 - Prob. 75ECh. 7.3 - Prob. 76ECh. 7.3 - Prob. 78ECh. 7.3 - Prob. 79ECh. 7.3 - Prob. 80ECh. 7.3 - Prob. 81ECh. 7.3 - Prob. 83ECh. 7.4 - Prob. 84ECh. 7.4 - Prob. 85ECh. 7.4 - Prob. 86ECh. 7.4 - Prob. 87ECh. 7.4 - Prob. 88ECh. 7.4 - Prob. 89ECh. 7.4 - Prob. 90ECh. 7.4 - Prob. 91ECh. 7.4 - Prob. 92ECh. 7.4 - Prob. 93ECh. 7.4 - Prob. 94ECh. 7.4 - Prob. 95ECh. 7.4 - Prob. 96ECh. 7.4 - Prob. 97ECh. 7.4 - Prob. 98ECh. 7.4 - Prob. 99ECh. 7.4 - Prob. 100ECh. 7.4 - Prob. 101ECh. 7.4 - Prob. 102ECh. 7.4 - Prob. 103ECh. 7.4 - Prob. 104ECh. 7.4 - Prob. 105ECh. 7.4 - Prob. 106ECh. 7.4 - Prob. 107ECh. 7.4 - Prob. 108ECh. 7.4 - Prob. 109ECh. 7.5 - Prob. 110ECh. 7.5 - Prob. 111ECh. 7.5 - Prob. 112ECh. 7.5 - Prob. 113ECh. 7.5 - Prob. 114ECh. 7.5 - Prob. 115ECh. 7.5 - Prob. 116ECh. 7.5 - Prob. 117ECh. 7.5 - Prob. 118ECh. 7.5 - Prob. 120ECh. 7.5 - Prob. 121ECh. 7.5 - Prob. 122ECh. 7 - Prob. 123CECh. 7 - Prob. 124CECh. 7 - Prob. 125CECh. 7 - Prob. 126CECh. 7 - Prob. 127CECh. 7 - Prob. 128CECh. 7 - Prob. 129CECh. 7 - Prob. 130CECh. 7 - Prob. 131CECh. 7 - Prob. 132CECh. 7 - Prob. 133CECh. 7 - Prob. 134CECh. 7 - Prob. 135CECh. 7 - Prob. 136CECh. 7 - Prob. 137CECh. 7 - Prob. 138CECh. 7 - Prob. 139CECh. 7 - Prob. 140CE
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