DSCI 2710 2nd EditionExam # 2 Study Guide Lectures: 6 - 8Lecture 6 Basic 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.P (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 B AAA7. 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 P(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 BABATwo 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) * P(B)Lecture 7P(M) = .20P(E) = .30P(MᴖE) = .10Random Variable – a function that assigns a numerical value to each outcome of an experiment.ProbabilityTTTTHTTTHHTTHHTHTHM M 20 8010 20 10 60EE 3070THHHHH 8 outcomesEx. The probability of having 3 H’s is 1/8.For every probability math function ideal with know how to calculate mean, std dev and variance. Know the center and how it varies (remember to put this on memory enhancement sheet.Lecture 8µ= Σx² P(x)Variance = [Σx²(P(x))] - µ²Binomial Random Variable- A Binomial Situation1. Your experiment consists of n repetitions, called trials2. Each trial has two mutually exclusive possible outcomes3. The n trials are independent4. The probability of a success of each trial is denoted p 5. (Fifth Step is in the book)Combination- C [the order doesn’t matter when you choose a sample]P(X=x) = nCx ( Px )(1-P)(n-x)µ = np ; variance = np(1 – P) ; standard deviation equals the square