Q. 50 50. Checking independence For ea... [FREE SOLUTION]

91影视

The Practice of Statistics for AP

David Moore,Daren Starnes,Dan Yates

$Math Studyset 91影视 Explanations$ Math

4th Edition 路 809 pages

ISBN: 9781319113339

Chapter 6: Q. 50 (page 379)

50. Checking independence For each of the following situations, would you expect the random variables $X$ and $Y$ to be independent? Explain your answers.
(a) $X$ is the rainfall (in inches) on November $6$ of this year, and $Y$ is the rainfall at the same location on November $6$ of next year.
(b) $X$ is the amount of rainfall today, and $Y$ is the rainfall at the same location tomorrow.
(c) $X$ is today's rainfall at the airport in Orlando, Florida, and $Y$ is today's rainfall at Disney World just outside Orlando.

Short Answer

Expert verified

(a) The amount of rainfall today $X$ and, the rainfall at the same location of next year $Y$ are not independent.

(b) The amount of rainfall today $X$ , and the rainfall at the same location tomorrow $Y$ are not independent.

Step by step solution

Part (a) Step 1: Given information

Here, $X$ is the rainfall (in inches) on November $6$ of this year, and $Y$ is the rainfall at the same location on November $6$ of next year.

Part (a) Step 2: Explanation

Rainfall on November $6^{t h}$ this year and the following year at the same spot.

Because the occurrences $X$ and $Y$ are linked to the particular location, they cannot be presumed to be independent. As a result, the two events are not independent

Part (b) Step 1: Given information

Let $X$ is the amount of rainfall today, and $Y$ is the rainfall at the same location tomorrow.

Part (b) Step 2: Explanation

Today and tomorrow, rain will fall at the identical place.

Because the occurrences $X$ and $Y$ are linked to a certain area, they cannot be considered independent. As a result, the two scenarios are not independent

Part (c) Step 1: Given information

Let $X$ is today's rainfall at the airport in Orlando, Florida, and $Y$ is today's rainfall at Disney World just outside Orlando.

Part (c) Step 2: Explanation

Today there was rain in the Orlando airport, as well as at Disneyland.

Because they are linked to specific locations, the events $X$ and $Y$ cannot be considered as separate. As a result, the two occurrences aren't independent.