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MATH 2600 Probability and Statistics Section 5-1 and 5-2 notes
Section 5-1 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 ___________________________________________.
Section 5-2 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 distinguishing 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; often expressed
in the format of a ________________________________
____________________________________ either a ______________ number of values or countable number of values, where “countable” refers to
the fact that there might be infinitely many values, but they result from a counting process
Example_______________________________________
_____________________________________ __________________ 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_______________________________________
Example 1 Discrete probability distribution
Requirements for Probability Distribution
- _________________________ where x assumes all possible values.
- _________________________ for every individual value of x.
Mean and Standard Deviation of a Probability Distribution
Mean = ___________________________________________
Standard Deviation = ________________________________
Directions to find the above mean and standard deviation on the Calculator
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ProbabilityDistribution as a table Values, x Probabilities, p ( x ) 0 _______ 1 _______ 2 _______
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 determining if they lie outside these limits: Maximum usual value = μ + 2 σ Minimum usual value = μ – 2 σ 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 correct. Unusually high: x successes among n trials is an unusually high number of successes if P ( x or more) ≤ 0.05. Unusually low: x successes among n trials is an unusually low number of successes if P ( x or fewer) ≤ 0.05.
Example 4 Discrete probability distribution The probability of being left handed is approximately 0.13. If you pick I pick 2 random students in class, find all value of probability of the random variable X = the number out of 2 students that is left- handed.
Example 5 Discrete probability distribution Jim is playing cards. He wants to know the probability drawing 0, 1, 2, or 3 aces out 3 cards drawn from a full deck. As a masterful statistics student, find the probabilities for him.
Expected Value (The average value of the outcomes) The expected value of a discrete random variable is denoted by E , and it represents the average value of the outcomes. It is obtained by finding the value of Σ [ x • P ( x )].
Section 5-2 assignment 1-5all, 7-16all, 19, 21, 22, 25, 27
