Using the random variables X and Y from Table 2.2, consider two new random variables W = 4 + 8X and V = 11 - 2Y. Compute (a) E(W) and E(V); (b) J2W and J2V; and (c) JWV and corr(W, V). TABLE 2.2 Joint Distribution of Weather Conditions and Commuting TimesRain (X = 0)0.15No Rain (X = 1)TotalLong commute (Y = 0)Short commute (Y = 1)0.070.220.150.630.78Total0.300.701.00

Given: two new random variables W = 4 + 8X V = 11 - 2Y To know the mean of W: E(W) = E(4 + 8X)…

Answered: TABLE 2.2 Joint Distribution of Weather…

TABLE 2.2 Joint Distribution of Weather Conditions and Commuting Times Rain (X = 0) 0.15 No Rain (X = 1) Total Long commute (Y = 0) Short commute (Y = 1) 0.07 0.22 0.15 0.63 0.78 Total 0.30 0.70 1.00

Principles of Economics 2e

2nd Edition

ISBN:9781947172364

Author:Steven A. Greenlaw; David Shapiro

Publisher:Steven A. Greenlaw; David Shapiro

ChapterA: The Use Of Mathematics In Principles Of Economics

Section: Chapter Questions

Problem 3RQ: Exercise A3 What dome slices of a pie chart represent?

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Concept explainers

Hypothesis Testing

In statistics, there are two ways to calculate the sample data. One is descriptive statistics and the other is inferential statistics. In descriptive statistics, all of the information is defined through graphs and charts. In inferential statistics, it allows one to test the hypothesis and it is always used to predict the data. Inferential statistics has two main areas: estimating parameters and hypothesis testing. A hypothesis is a statement about the unknown parameter of the population which we want to verify from the information available from the sample. The premise may or may not be true. The estimation of the whole population would be a reasonable way of deciding if the statistical hypothesis is valid. There are two types of hypotheses. They are null hypothesis and alternative hypothesis.

Question

Using the random variables X and Y from Table 2.2, consider two new random variables W = 4 + 8X and V = 11 - 2Y. Compute (a) E(W) and E(V); (b) J²_W and J²_V; and (c) J_WV and corr(W, V).

TABLE 2.2 Joint Distribution of Weather Conditions and Commuting Times
Rain (X = 0)
0.15
No Rain (X = 1)
Total
Long commute (Y = 0)
Short commute (Y = 1)
0.07
0.22
0.15
0.63
0.78
Total
0.30
0.70
1.00

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