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# Week 4 Of Notes STATS 220

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This 3 page Class Notes was uploaded by Christian Anthony on Monday February 8, 2016. The Class Notes belongs to 220 at James Madison University taught by Mr. Greg Jansen in Winter 2016. Since its upload, it has received 34 views. For similar materials see Elementary Statistics in Math at James Madison University.

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Date Created: 02/08/16

STATS NOTES 4 Feb. 1st and 3rd 4.1 Probability Probability- Chance behavior is unpredictable in the short run, but predictable in the long ru. Sample Space- A set of all possible outcomes of an experiment. Events- Outcomes of interest from a sample space. These are represented by any capital letter. (B for bunnies, F for food.) Set Notation- How a sample is written: {_,_,_,_,_} this example uses blanks instead of actual numbers. Keep in mind the brackets must be curly. {I’m serious.} EX:ssume we’re selecting from a list of all states that begin with an A. Find the EVENT that a state touches the Pacific. Sample: {AK,AL,AR,AZ} P(for Pacific): {AK} The PROBABILITY of an event is the proportion of times the event is expected to occur. For examples, heads and tails of a coin. The Probability of Heads is ½. P(H)=½ EX: ind the EVENT of rolling a fair die and getting an even number, and find its probability. S={1,2,3,4,5,6} E(for event)={2,4,6} P(for probability)= 3/6, or ½, or 50%. The formula for this process is simple, but I’ll put it here anyway: P(A)= The number of outcomes in A/the number outcomes in S *this formula only works if all outcomes are equally likely. PROPERTIES: ● 0≤ P(A) ≤ 1, inclusive. ● 0 means there is no chance, while 1 means something is guaranteed to occur. ● “Unusual Events”- these are events with less than a .005 percent chance of happening. *All of these points are only for THEORETICAL probability. EMPIRICAL PROBABILITY Repeating experiments many time, and using the proportion of times that a specific outcome occurs. EX: If there are 2,057,979 boys and 1,963,747 girls born in the US in 2002, determine the probability of a newborn being a boy. 2,057,979 4,021,726 = .517 Law of Large Numbers- As we repeat an experiment many times, the proportion of times the event occurs will approach its true probability. 4.2 Compound Events These use “and”/”or”. ● A and B ● A or C ● A and B and C These are ideas that combine one or more events at the same time. EX: ut of all 50 states, list those that touch the Pacific. List those that begin with A. Now list those that touch the Pacific AND begin with A. Then list those that begin with A OR touch the Pacific. A= {AL,AR,AK,AZ} P= {CA,OR,WA,HI,AL} A and P= {AL} A or P= {AL,AR,AK,AZ,CA,OR,WA,HI} CONTINGENCY TABLES: These are tables that display data: first data must be tallied, then counted, then put into these tables. EX: Young v. Old people, with high v. low blood pressure. HIGH BLOOD LOW BLOOD TOTALS PRESSURE PRESSURE YOUNG PEOPLE 82 125 207 OLD PEOPLE 74 89 163 TOTALS 156 214 370 1) How many people are young AND have high blood pressure? 82 2) How many people are young OR have high blood pressure? 281 3) Probability of Young AND High blood pressure? 82/370 *The P of (A or B)= P(A)+P(B)-P(A and B) Mutually Exclusive- Two events are mutually exclusive if they cannot occur at the same time. (Also called disjoint). The P(A and B)= 0. COMPLEMENTS: A complement is where an event doesn’t occur. So an A complement means A doesn’t happen. P(Ac )= 1-P(A) Random Variables: ● A numerical outcome of a probability experiment. ● The have an unknown outcome, but a known pattern of probabilities.

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