Probability and Statistics
Probability and Statistics MATH 2600
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This 3 page Class Notes was uploaded by Mrs. Kara Jacobs on Monday October 12, 2015. The Class Notes belongs to MATH 2600 at Georgia College & State University taught by Kenneth Flowers in Fall. Since its upload, it has received 8 views. For similar materials see /class/221926/math-2600-georgia-college-state-university in Mathematics (M) at Georgia College & State University.
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Date Created: 10/12/15
MATH 2600 Probability and Statistics Section 51 and 52 notes Section 51 Overview This chapter will deal with the construction of by combining the methods of descriptive statistics presented in Chapter 2 and 3 and those of probability presented in Chapter 4 Probability Distributions will describe what will happen instead of what actually happen Combining Descriptive Methods and Probabilities In this chapter we will construct by presenting outcomes along with the Chow s Cullecf sample 2 and 3 am r en K 93 statistics and graphs Chapter 5 Create a theoretical model describing how the experiment is Expected 0 behave H13quot w 52 ifs Farameers 1 x I Z 2011a am P 16 3 quot5 H 7 P216 Ii 15 7 l 39 5 6 Chapter I PWbab39WY 1 quot 5 16 1 an out Lyme P6 16 t Section 52 Random Variables This section introduces the important concept of a which gives the for value of a that is determined by chance Give consideration to distinguishng between outcomes that are likely to occur by chance and outcomes that are in the sense they are not likely to occur by chance a variable typically represented by that has a determined by chance of a procedure a description that gives the probability for each value of the random variable o en expressed in the format of a either a 7 i number of values or countable number of values where countable refers to the fact that there might be in nitely many values but they result from a counting process Example o 00 iii i many values and those values can be associated with measurements on a continuous scale in such a way that there are no gaps or interruptions Example Exam le 1 Discrete robabilit distribution Experiment Toss 2 Coins Let x the number of T s observed ProbabilityDistribution as a table x w x Valuesx ProbabilitiesI 21x1 i NA 0 a s 1 e l 2 r 4 5 0e 39 quotquot Re uirements for Probabilit Distribution 7777 Where x assumes all possible values iiiiii for every individual value of x Mean and Standard Deviation ofa Probability Distribution Mean Standard Deviation Directions to nd the above mean and standard deviation on the Calculator 1 Identifying Unusual Results Range Rule of Thumb According to the range rule of thumb most values should lie within 2 standard deviations of the mean We can therefore identify unusual values by 39 39 if they lie outside these limits Maximum usual value y 20 Minimum usual value y 20 Identifying Unusual Results Probabilities Rare Event Rule If under a given assumption such as the assumption that a coin is fair the probability of a particular observed event such as 992 heads in 1000 tosses of a coin is extremely small we conclude that the assumption is probably not 2 Unusually high Xsuccesses among ntrials is an unusually high number of successes if Px or more 5 005 1 Unusually low Xsuccesses among ntrials is an unusually low number of successes if Px or fewer S 005 Roundoff Rule for p and 039 Round results by carrying one more decimal place than the number of decimal places used for the random variable x If the values of x are integers round u and 039 to one decimal place Example 2 Discrete probability distribution 1 Create a probability distribution in the form of a table and a graph for the number of siblings a student has from the class data First de ne the random variable 2 Find the probability that a student has exactly 2 siblings 3 Find the probability that a student has 2 or less siblings 4 Find the probability that a student comes from a family with at least 6 kids Would this be considered unusual 5 Is this distribution skewed or approximately symmetric 6 Find the values that would be considered unusual from the mean and standard deviation How does this compare with nding the unusual values from the px Example 3 Discrete probability distribution 1 Suppose that you are playing a board game like Monopoly where you roll two dice add them up and then move that many spaces Make a probability distribution for the sum of two dice in the form of a table and graph First define a random variable 2 Is any sum considered unusual 3 Suppose that you need to roll at least a sum of 7 to stay out of bankruptcy in Monopoly What is the probability of rolling a sum of 7 or more 4 Would you consider this distribution perfectly symmetric approximately symmetric or skewed
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