ClassNotes-Chapter-05

# ClassNotes-Chapter-05 - Chapter 5 Discrete probability...

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1 © Sven Thommesen 2011 Chapter 5: Discrete probability distributions [Edited 6/25/09] INTRODUCTION: STATISTICAL EXPERIMENTS We have discussed the concept of a statistical experiment . That is an action or process which produces a specific outcome out of a set of possible outcomes every time the action or process is repeated. For any such statistical experiment, the set of possible outcomes is referred to as the sample space for that experiment. For the experiment “flip a coin” the sample space is the set {Heads, Tails}. In chapter 4 we focused on statistical experiments such as flipping a coin, rolling a die, spinning a roulette wheel, etc. Devices such as coins, dice, and roulette wheels are sometimes called “randomizing devices” because each possible outcome is equally likely (thus they follow the Classical method of assigning probability), and each repetition of the experiment is independent of the ones that went before. We also looked at experiments such as drawing cards out of a deck, or balls out of an urn. Depending on whether the card or ball that was drawn is put back or not, such experiments may be independent ( selection with replacement ) or not ( selection without replacement ). In all these kinds of experiments, the set of possible outcomes is small and countable, and we can assign to each outcome a unique whole number . (For example, the outcomes of the experiment „roll a die‟ can be numbered 1 through 6.) STATISTICAL VARIABLES If we perform a statistical experiment (such as rolling a die) a number of times and write down the outcome each time, we get a data set consisting of a number of observations, each containing data pertaining to one variable : the experimental outcomes. Let us name this variable “x”. For the following chapters, the “statistical experiments” we are interested in are not so much artificial experiments with randomizing devices, but rather measurements of the attributes of real- world entities: people‟s incomes, their shoe sizes, their GPAs, and so on. Or, they are the answers to survey questions we put to people.

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2 In these cases, the data generated or collected come in two distinct flavors: Discrete : where the variable “x” we are measuring comes in whole numbers ( integers ) only. Example: the number of students who show up for class each day, or any other case where we count something. Or it could be everyone‟s weight in pounds, if we round off our measurements to the nearest pound only. Continuous : where the variable “x” that we are measuring can take on any real number value: numbers that can take on any decimal or fractional value, not just integers. Examples: 2.5, - 3.75, 3.14159… Continuous data are usually the results of measurements: how tall, how far, how fast, what temperature, how long a time, etc.
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