Consider the following statements I through V. I. The possible values of outside temperature in Texas II. The...

Consider the following statements I through V.
I.        The possible values of outside temperature in Texas
II.      The sum of numbers on a pair of two dice
III.    The possible times that a person arrives at a restaurant
IV.    The possible sets of outcomes from flipping ten coins
V.      The possible sets of outcomes from flipping (countably) infinite coins

Which of the following “a through e” answer choices is incorrect?

		I is a description of a continuous random variable and III is a description of a continuous random variable
		II is a description of a discrete random variable and IV is a description of a discrete random variable
		IV is a description of a discrete random variable and V is a description of a discrete random variable
		I is a description of a continuous random variable and III is a description of a continuous random variable
		I is a description of a continuous random variable and III is a description of a discrete random variable

Expert Solution

Solution:

I. The possible values of outside temperature in Texas : Continuous Random Variable

Explanation: The outside temperature in Texas can take any fractional value also. It varies widely and can take up any value as it true for all the real numbers.

II. The sum of numbers on a pair of two dice: Discrete

Explanation: The sum of numbers on a pair of two dice is countable. It would take only a set finite discrete values.

III. The possible times that a person arrives at a restaurant : Discrete

Explanation: The number of times a person visits a place is easily countable and could take only set of definite values.

IV. The possible sets of outcomes from flipping ten coins: Discrete

Explanation: When we flip coins or roll a pair of dice, the outcomes are discrete as they can take up only some fixed values as their outcomes.

V. The possible sets of outcomes from flipping (countably) infinite coins : Discrete

Explanation: The possible set of outcomes from flipping countably infinite coins is also discrete as it might take long time to count all the possible outcomes, but it is possible to count the total number of outcomes possible.

Hence, the correct answer is: I is a description of continuous random variable and III is a description of Continuous random variable.

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