chp4 - 1 Chapter 4 Discrete Random Variables 4.1 Discrete...

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Unformatted text preview: 1 Chapter 4 Discrete Random Variables 4.1 Discrete and Continuous 4.2 Probability Distribution 4.3 Expectation and Variance 4.4 Binominal 4.5 Poisson 4.6 Hypergeometric Homework: 3,5,7,9,11,13,15,21,23,27,31, 43,52,53,61,63,68,69,77 2 Last chapter we discussed several useful concepts of dealing with probability problems. However, it is very difficult to write down sample spaces of some random experiments. In these cases the concept random variable is very useful. A random variable is a variable that assumes values associated with the random outcomes of a random experiment, where one and only one numerical values is assigned to each sample point. It is random because we can not predict the outcome of a random experiment. It is a variable because there are more than one possible sample points in a random experiment. 3 <Example 4.1>: (Basic) One hundred fair coins are tossed and the up faces are observed. (a) Is it convenient to write down the sample space for this random experiment? (b) Do we need to write down the sample space if we are interested in counting the number of heads in this random experiment? <Solutions>: (a) No, it takes vary long time to write the sample space of this random experiment. (b) No, we can use the concept of random variable to solve our problem. 4 Section 4.1: Discrete and Continuous Random Variable Some random variable can assume values on countable many numbers (such as integers) and some random variable can assume values on one or more intervals. For example, the distance between you home and UCF is between 0 and 100 miles that is an interval, i.e. the distance between your home and UCF is a continuous random variable. But the number of head in coin tossing experiment is a countable number, i.e. the number of heads in a coin tossing experiment is a discrete random variable . 5 <Example 4.2> (Basic) List five discrete random variables and five continuous random variables. 6 Sec 4.2: Probability Distributions for Discrete Random Variables This chapter will focus on the discussion of discrete random variable. A complete description of a discrete random variable requires that we specify all the possible values the random variable can assume and the probability associated with each value. Usually, we can use the following four steps to complete a probability table. Step 1 : Find out the variable of interest. Step 2 : List all the sample points in the sample space. Step 3 : List all the possible values of this random variable. Step 4 : Assign the probabilities to all the possible values. 7 <Example 4.3>: (Basic) A company has five applicants for two positions: three from UCF and two from UF. Suppose that the five applicants are equally qualified and no preference is given for choosing either school. Let x be the number of UCF graduates chosen to fill the two positions....
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chp4 - 1 Chapter 4 Discrete Random Variables 4.1 Discrete...

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