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Discrete probability distributions

# Discrete probability distributions - Chapter 4 Discrete...

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Chapter 4 – Discrete Probability Distributions 4.1 Probability Distributions: Random Variables A random variable is a variable whose value depends on the outcome of a probability experiment. As in algebra, random variables are represented by letters. Examples: T = the number of tails when a coin is flipped 3 times. s = the sum of the values showing when two dice are rolled. h = the height of a woman chosen at random from a group. V = the liquid volume of soda in a can marked 12 oz. There are two basic types of random variables: Discrete Random Variables – (counted data) have a finite or countable number of possible values. (Number of people in a class.) Continuous Random Variables – (measured data) can take on any value in some interval. (Average weekly study hours of people in a class.) Examples: The variables ____ and _____ from above are discrete random variables The variables _____ and _____ from above are continuous random variables. In chapter 4 we will focus on DISCRETE random variables, in chapter 5 we will look at continuous random variables. 1

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Probability Distributions of Discrete Random Variables: A probability distribution for a discrete random variable x is a list of each possible value for x together with the probability that when the experiment is run, x will have that value. This probability is denoted by ( ) P x . Examples: As above, let T be the random variable that represents the number of tails obtained when a coin is flipped three times. Then T has 4 possible values: 0, 1, 2, and 3. The probability distribution for T is given in the following table: T 0 1 2 3 P(T) (fraction) A statistics class of 25 students is given a 5 point quiz. 3 students scored 0, 1 scored 1, 4 scored 2, 8 scored 3, 6 scored 4, and 3 students scored 5. If a student is chosen at random, and the random variable s is the student’s quiz score then the probability distribution of s is: s 0 1 2 3 4 5 P(s) (decimal) Note: For any discrete random variable x : 0 ( ) 1 P x and ( ) 1 P x = Finding Probabilities from a Probability Distribution: 2
Since a random variable can only take on one value at a time, the events of a variable assuming two different values are always mutually exclusive . The probability of the variable taking on any number of different values can thus be found by simply adding the appropriate probabilities. Exercises: Find the probability that a student scored 3 or more on the quiz from the previous example. Find the probability that a student did not get a perfect score. Find the probability of getting 2 or more tails when a coin is flipped 3 times. Find the probability of getting at least one tail. Find the missing probability in the following distribution: X -3 0 5 13 ( ) P X 0.21 0.15 0.33 Mean or Expected Value: 3

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The mean or expected value of a random variable x is the average value that we should expect for x over many trials of the experiment.
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Discrete probability distributions - Chapter 4 Discrete...

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