Calculate expected values and use them to solve problems
(+) Define a random variable for a quantity of interest by assigning a numerical value to each event in a sample space; graph the corresponding probability distribution using the same graphical displays as for data distributions.
| Content | Skills | Learning Targets | Big Ideas | Essential Questions |
|---|---|---|---|---|
|
3 - Define (random variable for quantity of interest)
2 - Assign (numerical value to each event in sample space)
3 - Graph (probability distribution corresponding to interest random variable using data distribution graphical displays)
|
3 - I can define a random variable for a quantity of interest.
2 - I can assign a numerical value to each event in a sample space.
3 - I can graph probability distributions for a random variable using the same graphical displays as for data distributions.
|
A. A random variable can be defined for a quantity of interest by assigning a numerical value to each event in a sample space.
B. A corresponding probability distribution for defined random variable can be graphed using the same graphical displays as for data distributions.
|
A.1 What is a random variable?
A.2 How can a random variable for a quantity of interest be defined?
B.1 How can a probability distribution corresponding to a defined random variable be graphed with data distribution displays?
|
(+) Calculate the expected value of a random variable; interpret it as the mean of the probability distribution.
| Content | Skills | Learning Targets | Big Ideas | Essential Questions |
|---|---|---|---|---|
|
Value
Variable
Mean Distribution
|
3 - Calculate (expected value of random variable)
4 - Interpret (expected value as mean of probability distribution)
|
3 - I can calculate (expected value of random variable.
4 - I can interpret the expected value of a random variable as the calculated mean of a probability distribution.
|
A. Calculated expected values of random variables can be interpreted as the mean of a probability distribution.
|
A.1 Why can the expected value of a random variable be interpreted as the mean of a probability distribution?
|
(+) Develop a probability distribution for a random variable defined for a sample space in which theoretical probabilities can be calculated; find the expected value.
For example, find the theoretical probability distribution for the number of correct answers obtained by guessing on all five questions of a multiple-choice test where each question has four choices, and find the expected grade under various grading schemes.
| Content | Skills | Learning Targets | Big Ideas | Essential Questions |
|---|---|---|---|---|
|
Random Variable
|
4 - Develop (probability distribution for a random variable)
3 - Calculate (theoretical probabilities)
3 - Find (expected value)
|
4 - I can develop a probability distribution for a random variable defined for a sample space of theoretical probabilities.
3 - I can calculate theoretical probabilities.
3 - I can find expected values.
|
A. A probability distribution can be developed for a random variable defined for a sample space in which theoretical probabilities can be calculated.
B. Expected values can be found by using a theoretical probability distribution.
|
A.1 How can a probability distribution be developed for a random variable defined for a sample space of theoretical probabilities?
B.1 How can the expected value be found using a theoretical probability distribution?
|
(+) Develop a probability distribution for a random variable defined for a sample space in which probabilities are assigned empirically; find the expected value.
For example, find a current data distribution on the number of TV sets per household in the United States, and calculate the expected number of sets per household. How many TV sets would you expect to find in 100 randomly selected households?
| Content | Skills | Learning Targets | Big Ideas | Essential Questions |
|---|---|---|---|---|
|
Random Variable
|
4 - Develop (probability distribution for random variable)
3 - Assign (probabilities empirically)
3 - Find (expected value)
|
4 - I can develop a probability distribution for a random variable for a sample space of empirically assigned probabilities.
3 - I can assign probabilities empirically.
3 - I can find expected value.
|
A. A probability distribution can be developed for a random variable defined for a sample space in which probabilities are assigned empirically.
B. Expected values can be found by using a probability distribution of empirically assigned values.
|
A.1 What is the meaning of an empirically assigned probability?
A.2 How can a probability distribution be developed for a random variable defined for a sample space of empirically assigned probabilities?
B.1 How can an expected value be found using a probability distribution of empirically assigned values?
|
Use probability to evaluate outcomes of decisions
(+) Weigh the possible outcomes of a decision by assigning probabilities to payoff values and finding expected values.
| Content | Skills | Learning Targets | Big Ideas | Essential Questions |
|---|---|---|---|---|
|
3 - Weigh (possible outcomes of decision)
3 - Find (expected values)
2 - Assign (probabilities to payoff values)
3 - Find (expected payoff for game of chance [a])
5 - Evaluate (strategies based on expected values [b])
2 - Compare (strategies based on expected values [b])
|
3 - I can weigh the possible outcomes of decision.
3 - I can find expected values.
2 - I can assign probabilities to payoff values.
3 - I can find expected values.
5 - I can evaluate strategies based on expected values [b].
2 - I can compare strategies based on expected values [b].
|
A. One can make better decisions by figuring the probability of the possible outcomes.
B. One can determine appropriate strategies based upon expected values.
|
A.1 How can I use probability in decision making?
B.1 How can probability help me when choosing a strategy?
|
(+) Use probabilities to make fair decisions (e.g., drawing by lots, using a random number generator).
| Content | Skills | Learning Targets | Big Ideas | Essential Questions |
|---|---|---|---|---|
|
Probabilities
|
3 - Use (probabilities, including drawing by lots and random number generator)
5 - Make (fair decisions using probability)
|
3 - I can use various probabilities.
5 - I can make fair decisions through the use of drawing by lots and random number generators.
|
A. Probabilities, including drawing by lots and random number generators, can be utilized to make fair decisions.
|
A.1 What is the meaning of a fair decision?
A.2 What is the meaning of drawing by lots?
A.3 What is a random number generator?
A.4 How can fair decisions be made using probabilities?
|
(+) Analyze decisions and strategies using probability concepts (e.g., product testing, medical testing, pulling a hockey goalie at the end of a game).
| Content | Skills | Learning Targets | Big Ideas | Essential Questions |
|---|---|---|---|---|
|
Probability concepts
|
3 - Use (probability concepts)
4 - Analyze (decisions and strategies)
|
3 - I can use various probability concepts.
4 - I can analyze decisions and strategies related to product testing, medical testing, and sports.
|
A. Probability concepts can be used to analyze decisions and strategies related to real-world situations.
|
A.1 In what ways can probability concepts be used to analyze decisions and strategies related to real-world situations?
|
Be the first to comment below.