Untitled Lesson

Graphing

y=3x^2

Multiple Choice

Which of the following is NOT typically associated with discrete random variables?

• Probability density function (PDF)

• Cumulative distribution function (CDF)

• Mean, variance and standard variation

• Differential equations

Open Ended

Why is it important for engineers to understand the concept of random variables in mathematics?

Multiple Choice

Which of the following best describes the role of statistics and probability in engineering as shown in the diagram?

• They are used only to confirm solutions.

• They are used to conduct experiments and refine models.

• They are used only to develop a clear description.

• They are used only to make recommendations.

Open Ended

Explain how probability provides a bridge between descriptive and inferential statistics.

Fill in the Blank

Statistics is the scientific application of mathematical principles to the collection, analysis, and presentation of ___.

Fill in the Blank

A sample is a subset of the ___.

Multiple Choice

Which of the following best describes a random variable (RV)?

• A variable that assumes any of several different values as a result of some random event or experiment

• A group of individuals that share one or more characteristics

• A subset of the population

• The set of all possible outcomes of an experiment

Open Ended

Explain the difference between a sample and a population, and why it is important to distinguish between the two in statistical studies.

Multiple Choice

What does the relative frequency (f/n) approximate as the sample size n gets larger?

• Probability

• Sample space

• Population size

• Random variable

Multiple Choice

Which of the following statements about mutually exclusive events is correct?

• If one event occurs, the other cannot occur.

• Both events can occur at the same time.

• The events are always independent.

• The events must have the same probability.

Reorder

Reorder the following

• One

• Two

• Three

• Four

• Five

1

2

3

4

5

• 1
• 2
• 3
• 4
• 5

Multiple Select

Which of the following are examples of events in the experiment of tossing a die?

• Observe an odd number

• Observe a number greater than 2

• Observe a 6

• Observe a person is 30 years old

Multiple Choice

Which of the following best describes a sample space when tossing a single die?

• All possible outcomes of the die toss

• Only the odd numbers on the die

• Only the even numbers on the die

• The probability of each outcome

Multiple Select

Based on the die toss example, which of the following are included in event B (a number greater than 2)?

• E3

• E4

• E5

• E1

Open Ended

Explain how the probability of an event is determined using relative frequency, as described in the slides.

Fill in the Blank

The sum of the probabilities for all simple events in a sample space S equals ___.

Multiple Choice

Which of the following is an example of a probability estimated from empirical studies?

• P(Head) = 1/2

• P(Black hair) = .90

• P(Tail) = 1/2

• P(Even number) = 1/2

Multiple Choice

If all simple events in an experiment are equally likely, what is the formula for the probability of event A?

• Number of simple events in A / Total number of simple events

• Number of times event A occurs / Number of times of an experiment

• Number of favorable outcomes / Number of unfavorable outcomes

• Total number of outcomes / Number of experiments

Math Response

Toss a fair coin twice. What is the probability of observing at least one head?

Type answer here

Correct Answer: 0.75

Deg^°

Rad

Multiple Choice

Which of the following is NOT a possible outcome when tossing a fair coin twice?

• HT

• TH

• TT

• HHH

Multiple Choice

What is the total number of possible outcomes when throwing a pair of dice?

• 6

• 12

• 24

• 36

Multiple Choice

Which events have the same probability when throwing a pair of dice according to the table?

• Dice add to 3 and Dice add to 6

• Red die shows 1 and Green die shows 1

• Dice add to 6 and Red die shows 1

• Dice add to 3 and Green die shows 1

Open Ended

An experiment of tossing a fair coin three times. Let X be a random variable of getting head. Find the probability of getting head by using probability distribution function (PDF) table, graph and equation.

Draw

Make x^2

Fill in the Blank

Fill in the blank: The probability of getting exactly two heads when tossing a fair coin three times is ___

Open Ended

After learning about random variables, what is one question you still have or a concept you would like to explore further?

Multiple Choice

What is the difference between discrete and continuous random variables as discussed in this chapter?

• Discrete random variables take specific values, while continuous random variables can take any value within a range.

• Discrete random variables are always integers, while continuous random variables are always fractions.

• Discrete random variables are used in statistics, while continuous random variables are used in engineering.

• Discrete random variables have no probability density function, while continuous random variables do.