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50. Checking independence For each of the following situations, would you expect the random variables Xand Yto be independent? Explain your answers.

(a)Xis the rainfall (in inches) on November 6of this year, and Yis the rainfall at the same location on November 6 of next year.
(b) Xis the amount of rainfall today, and Y is the rainfall at the same location tomorrow.
(c) Xis 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 Xand, the rainfall at the same location of next yearYare not independent.

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

(c) The rainfall at the airport Xand rainfall at Disney World Yare not independent.

Step by step solution

01

Part (a) Step 1: Given information 

Here, Xis the rainfall (in inches) on November 6of this year, and Yis the rainfall at the same location on November 6of next year.

02

Part (a) Step 2: Explanation 

Rainfall on November 6ththis year and the following year at the same spot.

Because the occurrences Xand Yare linked to the particular location, they cannot be presumed to be independent. As a result, the two events are not independent

03

Part (b) Step 1: Given information 

Let Xis the amount of rainfall today, and Yis the rainfall at the same location tomorrow.

04

Part (b) Step 2: Explanation 

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

Because the occurrences Xand Yare linked to a certain area, they cannot be considered independent. As a result, the two scenarios are not independent

05

Part (c) Step 1: Given information 

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

06

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 Xand Ycannot be considered as separate. As a result, the two occurrences aren't independent.

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