DSCI 2710 6th Edition Lecture 6Outline of Last Lecture I. Time SeriesII. TrendIII. Seasonality IV. CyclicalV. Irregular activityOutline of Current Lecture VI. Basic Laws of ProbabilityCurrent LectureBasic Laws of probability1. If the probability of an event is 1.0 then the event must occur.2. If the probability of an event is -0- then the event will never occur.3. The probability of any event must assume a value between 0 and 1.0 inclusive.4. The sum of the probabilities of all simple events in a sample space must be equal to 1.0.Experiment – an activity for which the outcome is uncertainEvent – consists of one or more possible outcomesWhen you estimate probability you are estimating the probability of an eventRelative Frequency Approach – (estimating probability) based on observing the experiment n times and counting the number of times an event occurs.Subjective Probability – it is a measure that a particular event will occur. A value of one indicatesthat you believe this event will occur with complete certainty.5. Events A and B are mutually exclusive if they have no other elements in common.These notes represent a detailed interpretation of the professor’s lecture. GradeBuddy is best used as a supplement to your own notes, not as a substitute. B AP (A ᴗ B) = P(A) + P(B) ᴗ- unionComplement6. If the complement of an event A is the set of all outcomes not in AP(A) + P(A) = 1 7. Probability of A or B.P (A ᴗ B)= P (A) + P(B) – P (Aᴖ B) ᴖ - intersect AᴗBNote: is still works if they are mutually exclusive. Then P (Aᴖ B) = 08. Conditional ProbabilityProbability of A given B AABABAP(A|B) = P(AᴖB)/P(B)9. Dependence – if the occurrence of one event alters the probability of another event. If events are dependent then for 2 dependent events P(AᴖB)= P (A) * P(B|A)Or P(AᴖB) = P(B) * P(A|B)10. Independence probability Two events are independent if the occurrence of one event does not alter the probability of another one. P(A|B) = P(A)P(B|A) = P(B)Multiplication rule for any two independent events P(AᴖB) –= P(A) *