statistics notes

statistics notes - STAT 2000 Probability and Probability...

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STAT 2000 Probability and Probability Distributions Spring 2011

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Identify Objective What do you want to find out? Design Study and Collect Data Select a Sample from a Population Describe Data Organize, present the data you collect. Make Inferences about a Population Make predictions about the Population based on data from the Sample. Principles of Probability The Process of a Statistical Study
Terminology and Definitions : Tossing a coin would be considered a random phenomenon because the outcome is uncertain. It could be heads or it could be tails. Probability is a way of measuring this uncertainty. If we toss a balanced coin 4 times, we are not assured of getting exactly two heads and two tails. But if we toss a balanced coin a large number of times …

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According to the Law of Large Numbers , if we repeatedly toss a balanced coin, the proportion of times a head will occur will get closer and closer to 0.5. We call this number the probability of getting a head. The probability of an outcome is the proportion of times the outcome would occur if the random phenomenon was repeated a large number of times. It is a long run proportion.
Rosencrantz and Guildenstern are two well-dressed Elizabethan men in the middle of a coin-spinning game. Whoever calls the coin correctly wins it, and Rosencrantz has been calling heads and winning dozens of times. While he feels guilty about taking so much money from his friend, he does not see the consistent "heads" tosses as peculiar at all. Conversely, Guildenstern doesn't care about the money, but he is disturbed by the lengthening series of "heads" tosses. Rosencrantz calls out that heads has come up eighty-five times: a new record for him. Rosencrantz and Guildenstern Are Dead , by Tom Stoppard

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It is not always possible to repeat a random phenomenon a large number of times to determine objective information. Sometimes we have to rely on subjective probability. For example: If I drive to class today, what is the probability that I will find a parking place quickly? In addition, we can also rely on probability properties and rules. This is what we will learn about in this section.
Terminology and Examples A sample space is the set of all possible outcomes of a random phenomenon. (It is denoted S.) Ex: Toss a coin. S = {H, T} Ex: Toss a die. S = {1, 2, 3, 4, 5, 6} An event is a subset of the sample space. Ex: Toss a die. Let E be the event an even number is observed. E = {2, 4, 6}

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If the individual outcomes are equally likely, P(E) = # of outcomes in the event E # of outcomes in the sample space = # of outcomes favorable to E total # of outcomes Let E be the event, getting an even number of dots on a die. E = {2, 4, 6} P(E) = 3/6
Toss two balanced coins. What is the sample space?

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statistics notes - STAT 2000 Probability and Probability...

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