STAT #1

Multiple Choice

Which of the following best describes a random variable?

• A variable whose value is determined by chance

• A variable that always has a fixed value

• A variable that can only take positive values

• A variable that is always continuous

Open Ended

Why do you think understanding random variables is important in real-life situations?

Multiple Choice

Which of the following best defines a sample space in probability?

• The set of all possible outcomes of an experiment

• The most likely outcome of an experiment

• The outcome with the highest probability

• The set of all favorable outcomes

Open Ended

If three coins are tossed, what numbers can be assigned for the frequency of heads that will occur?

Multiple Select

Which of the following are possible outcomes when three cell phones are tested for defects?

• NNN

• NND

• DDD

• NDN

Open Ended

Explain how the concept of random variables helps in assigning values to outcomes in a sample space. Use the example of testing three cell phones for defects.

Multiple Choice

Based on the table, what value does the random variable X take for the outcome 'DND'?

• 1

• 2

• 3

• 0

Multiple Choice

What is a random variable?

• A variable that always takes the same value

• A function that associates a real number to each element in the sample space

• A variable whose values are always integers

• A function that only works with heads in coin tosses

Open Ended

Explain the steps to determine the values of a random variable in a coin tossing experiment.

Multiple Choice

After tossing three coins, what are the possible values that the random variable Y (number of tails) can take?

• 0, 1, 2, 3

• 1, 2, 3, 4

• 0, 1, 2

• 1, 2, 3

Multiple Select

Which of the following are possible outcomes when two balls are drawn from an urn containing red and blue balls?

• RR

• RB

• BB

• BR

Multiple Choice

Which of the following best describes a discrete random variable?

• A variable that can take any value on a continuous scale

• A variable whose possible outcomes are countable

• A variable that cannot be measured

• A variable that only takes negative values

Multiple Choice

Which of the following scenarios best illustrates a discrete random variable?

• The time taken for a chemical reaction to complete

• The number of students absent in a class

• The temperature recorded at noon

• The distance a car travels on a full tank

Multiple Select

Which of the following are examples of continuous random variables?

• Number of defective chairs produced in a factory

• Heights of students in a class

• Number of heads in a coin toss

• Weights of apples

Open Ended

Suppose you are conducting an experiment to measure the amount of rainfall in a city over a month. Is the amount of rainfall a discrete or continuous random variable? Justify your answer.

Open Ended

Classify the following random variables as discrete or continuous. a) the number of defective computers produced by a manufacturer b) the weight of newborns each year in a hospital c) the number of siblings in a family of a region d) the amount of paint utilized in a building project e) the number of dropout in a school district for a period of 10 years

Multiple Select

Select all statements that correctly describe discrete and continuous random variables.

• Discrete random variables represent count data and have countable outcomes.

• Continuous random variables take values on a continuous scale and represent measured data.

• Discrete random variables can only take values between 0 and 1.

• Continuous random variables are always integers.

Open Ended

What questions do you still have about random variables or their classification as discrete or continuous?

Multiple Choice

Which of the following is NOT an objective of this lesson on random variables?

• Illustrate a random variable

• Classify random variables as discrete or continuous

• Find the possible values of a random variable

• Calculate the mean of a random variable