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Lecture 03: Probability and Simulation Lecture 03: Probability and Simulation
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Sign in to readLecture 03: Probability and Simulation
Probability and Statistical Inference
Probability Terminology
Three Interpretations of Probability
Video Screen Tension: Data and Single Draws
Exercises (a)–(d)
Combining Events
Addition and Complement Rules
Conditional Probability and Multiplication
Video Screen Tension: Two Draws Without Replacement
(e) A High-Tension Screen Has Already Been Removed
(f) Both Screens Exceed 320
(g) Neither Screen Exceeds 320
(h) Exactly One Screen Exceeds 320
Hypothetical Mammogram Table
(a) Marginal Probabilities
(b) Cancer or a Positive Mammogram
(c) Are Cancer and a Negative Mammogram Mutually Exclusive?
(d) Cancer Given a Positive Mammogram
(e) A Positive Mammogram Given Cancer
(f) Cancer and a Positive Mammogram
(g) Two People Without Cancer
Independence
Exercise: Freshman Standing and Age 21
Screen Exercise (i): Sampling With Replacement
When Is Independence a Useful Approximation?
Are Cancer and a Positive Mammogram Independent?
Screen Exercise (j): Verify by Simulation in R
How the Companion Worksheet’s Loops Work
Manufacturing Machinery Example
Exercises (a)–(e)
(f) Are Murgh and Perfect Condition Independent?
Circuit Example: Three Components in Parallel
(a) No Components Fail
(b) Exactly One Component Fails
(c) Are Two Failures Strong Evidence of a Higher Failure Rate?
(d) The System Still Functions
R Check and Simulation
Choosing a Probability Rule