A craps player rolls two six-sided dice. X is the distance between the centers of the two dice after they come to a rest. Is the random variable X discrete or continuous? Choices: (A)discrete (B)continuous

Range of X: X can take on any value within a range because the distance between the centers of two dice can be any real number depending on how they land.Countability of X: Since X can be any real number within a range, it is not countable like whole numbers. It's more like measuring something with a ruler where you can get all sorts of decimals.Discreteness of X: So, X is not just 1, 2, 3, and so on, it can be like 1.5, 2.34, or whatever, which means it's not discrete.Comparison with Discrete Random Variables: Discrete random variables are only for things you can count using whole numbers, but continuous random variables are for measurements that can be any value in a range, like lengths or distances.Classification of X: Therefore, X is a continuous random variable because it represents a measurement that can take on any value within a range.

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A craps player rolls two six-sided dice. $X$ is the distance between the centers of the two dice after they come to a rest. $\newline$ Is the random variable $X$ discrete or continuous? $\newline$ Choices: $\newline$ (A) discrete $\newline$ (B) continuous

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Algebra 2

Identify discrete and continuous random variables

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Q. A craps player rolls two six-sided dice.

X

is the distance between the centers of the two dice after they come to a rest.

\newline

Is the random variable

X

discrete or continuous?

\newline

Choices:

\newline

(A) discrete

\newline

(B) continuous

Range of $X$ : $X$ can take on any value within a range because the distance between the centers of two dice can be any real number depending on how they land.
Countability of $X$ : Since $X$ can be any real number within a range, it is not countable like whole numbers. It's more like measuring something with a ruler where you can get all sorts of decimals.
Discreteness of X: So, $X$ is not just $1$ , $2$ , $3$ , and so on, it can be like $1.5$ , $2.34$ , or whatever, which means it's not discrete.
Comparison with Discrete Random Variables: Discrete random variables are only for things you can count using whole numbers, but continuous random variables are for measurements that can be any value in a range, like lengths or distances.
Classification of $X$ : Therefore, $X$ is a continuous random variable because it represents a measurement that can take on any value within a range.