IPS - Day 37

This was the start of a two-day review prior to the mid-term exam at the end of this week.

Rather than repeat myself about the structure of the review process and its origin, I refer you to my Discrete Math post which goes into how the review process works.

For this class, I provided four topic areas and first asked students to come up with the top five concepts, ideas, or formulas that we have studied so far. Then I had students share out their ideas in their groups. The groups then worked on creating a list of five items under each of the four given topics.

Conditional Probability and Independence

• Two or more variables relate to each other
• P(A and B) / P(B) = P(A|B)
• Independent means that event A is not relevant to event B
• To show independence show that P(A)P(B) = P(A and B)
• Conditional probability is when one event occurs assuming a past event occurred

Expected Value

• Simulations
• Outcomes
• E(X) = Sum of xP(X=x)
• Random numbers
• Mean
• Sounding the Alarm investigation
• Deal or No Deal investigation
• Probability models

Probability

• Rules
• Tree Diagram
• Venn Diagram
• Random integers
• Tables
• Probability Model
• Law of large numbers
• Drawing cards and rolling dice
• Experimental versus theoretical probability
• Theoretical probability = number of favorable outcome / total outcomes
• Mutually exclusive events
• If A and B are mutually exclusive then P(A or B) = P(A) + P(B)
• Independent events
• If A and B are independent then P(A and B) = P(A)P(B)

Sampling and Bias

• Bias is when one answer seems better than other answers
• Random / equal chances
• Random samples are not biased
• Surveys
• Error is expected
• Observational study
• Sample size can be small if representative
• Sample types: cluster, stratified, systematic, SRS, multi-stage

Groups were then asked to develop problems for the different categories that will be presented to the class next period. The groups needed to answer the questions they developed. These questions will be the review problems that students will work on.

Visit the class summary for a student's perspective and to view the lesson slides.