Question

Solar Eclipses. The World Almanac provides information on past and projected total solar eclipses from 1955 to 2015. Unlike total lunar eclipses, observing a total solar eclipse from Earth is rare because it can be seen along only a very narrow path and for only a short period of time.

a. Let X denote the duration, in minutes, of a total solar eclipse. Is X a discrete random variable? Explain your answer.

b. Let Y denote the duration, to the nearest minute, of a total solar eclipse. Is Y a discrete random variable? Explain your answer.

Short answer

Part a. No

Part b. Yes

Step-by-step solution

Part (a) Step 1. Given information

From 1955 through 2015, there were total solar eclipses. Observing a total solar eclipse from Earth is unusual, unlike total lunar eclipses, because it can only be viewed along a very limited path and for a brief period of time.

Let signify the length of a total solar eclipse in minutes.

Part (a) Step 2. Solution

No, because the time duration can only be measured as a single value within a given time range. The time can have as many decimal places as the measurement precision allows.

Part (b) Step 1. Solution 

Yes, because it will take countable integer values, it is a random variable.