# FREE PMF Discrete Random Variables Questions and Answers

#### An example of a continuous variable is...

A continuous variable is one that can take on any value within a certain range. In this case, distance is a continuous variable because it can be measured in any unit of length and can have any value within that unit. Acceleration, force, and power, on the other hand, are not continuous variables as they have specific units and can only take on certain values within those units.

#### Which is a type of random variables?

A continuous random variable is a type of random variable that can take on any value within a certain range or interval. It can have an infinite number of possible outcomes and is typically associated with measurements or quantities that can be expressed as real numbers. Examples of continuous random variables include height, weight, time, and temperature. In contrast, other options like linear, normal, and ordinal are not types of random variables but rather describe different characteristics or properties of random variables.

#### A random variable can also be referred to as...

A random variable can also be referred to as "stochastic" because it represents a variable whose outcome is determined by chance or probability. Stochastic variables are used in probability theory and statistics to model and analyze uncertain events or processes. They can take on different values with varying probabilities, and their behavior is often described using probability distributions.

#### If a variable can take on any value between two specified values, it is called...

A continuous variable is a variable that can take on any value within a specified range. Unlike discrete variables, which can only take on specific values, a continuous variable can take on any value within a range, including decimal values. In this case, the variable can take on any value between two specified values, indicating that it is a continuous variable.

#### A variable whose possible values are numerical outcomes of a random phenomenon is termed...

A random variable is a term used to describe a variable that can take on different numerical outcomes as a result of a random or uncertain event or phenomenon. This means that the values of the variable are not predetermined or fixed, but rather depend on the outcome of the random process. Therefore, the correct answer is "Random variable."

#### Which of these restricts the measurement of a continuous variable?

Accuracy restricts the measurement of a continuous variable because accuracy refers to the degree of closeness between a measured value and the true value of the variable. In the context of measurement, accuracy determines how precise and reliable the measurement is. Therefore, if the accuracy is low, it means that the measurement may have a larger margin of error, limiting the ability to accurately measure and quantify the continuous variable.

#### Random variables that can assume only a countable number of values are called...

Random variables that can assume only a countable number of values are called discrete. Discrete random variables have specific, separate, and distinct values. They can be expressed as whole numbers or a finite set of values. Unlike continuous random variables, discrete random variables cannot take on any value within a given range.

#### Random variables that can take on any of the countless number of values in an interval are called...

Random variables that can take on any of the countless number of values in an interval are called continuous. This means that the variable can take on any value within a range, including fractions and decimals. Unlike discrete variables, which can only take on specific, separate values, continuous variables have an infinite number of possible values. Closed and open are not appropriate terms to describe random variables, as they refer to intervals rather than the variables themselves.

#### The qualities of discrete data can be:

Discrete data refers to data that can only take on specific values and cannot be measured on a continuous scale. It can only be counted or enumerated. This means that the values of discrete data can be expressed as whole numbers or integers, such as the number of students in a class or the number of cars in a parking lot. Therefore, the correct answer is "Counted."

#### A random variable which takes values greater than or equal to zero with probability one is...

A random variable that takes values greater than or equal to zero with probability one is referred to as nonnegative. This means that the variable cannot have negative values and is restricted to zero or positive values only.

#### Variables which cannot take any value at all are...

Nonrandom variables are those that do not have any variation or variability in their values. In other words, these variables cannot take on different values and remain constant. They are fixed and unchanging. In contrast, random variables can take on different values based on chance or probability. Therefore, nonrandom variables cannot take any value at all, as they are not subject to variation or randomness.