Discrete vs continuous classify the following as

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Discrete vs ContinuousClassify the following as discrete or continuous Length of your left thumb Number of children in a family Number of devices in the house that connect to the Internet Sodium concentration in the bloodstream
Discrete Probability Distributions The most common way to display a pdf for discrete data is with a table The probability distribution table always has two columns (or rows) The first, x, displays all the possible outcomes The second, P(x), displays the probabilities for these outcomes
Examples of Probability DistributionsImportant: The sum of all the probabilities must equal 1
Example - Playing DiceRoll a fair six-sided die. You will win $4 if you roll a 5 or a 6. You will lose $5 if you roll a 1. You will lose $1 if you roll a 2. Any other outcome, you will win or lose $0. What is the probability distribution table for the amount you will win?
The Binomial ModelThe binomial probability distribution is a discrete probability distribution function Useful in many situations where you have numerical variables that are counts or whole numbersSurprise! Classic application of the binomial model is counting heads when flipping a coin
The Binomial ModelThe binomial model provides probabilities for random experiments in which you are counting the number of successes that occur. Four characteristics must be present:
Binomial or Not?40 randomly selected college students were asked if they selected their major in order to get a good job. 35 randomly selected Americans were asked what country their mothers were born. To estimate the probability that students will pass an exam, the professor records a study group's success on the exam.
Computing Binomial ProbabilitiesA Stats 10 test has 4 multiple choice questions with four choices with one correct answer each. If we just randomly guess on each of the 4 questions, what is the probability that you get exactly 3 questions correct? There are 4 different outcomes in which you could get 3 of 4 questions correct: Correct, Correct, Correct, Wrong Correct, Correct, Wrong, Correct Correct, Wrong, Correct, Correct Wrong, Correct, Correct, Correct
Computing Binomial ProbabilitiesA Stats 10 test has 4 multiple choice questions with four choices with one correct answer each. If we just randomly guess on each of the 4 questions, what is the probability that you get exactly 1 question correct? Correct, Correct, Correct, Wrong = 0.25 x 0.25 x 0.25 x 0.75= 0.01172 The four outcomes all have the same probability so the probability that you get exactly 3 correct is 4 x 0.01172 = 0.04668

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