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14111cn8.1-2 - of real numbers(i.e usually measurements...

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c Kendra Kilmer October 27, 2011 Section 8.1 - Distributions of Random Variables Definition : A random variable is a rule that assigns a number to each outcome of an experiment. Example 1 : Suppose we toss a coin three times. Then we could define the random variable X to represent the number of times we get tails. Example 2 : Suppose we roll a die until a 5 is facing up. Then we could define the random variable Y to represent the number of times we rolled the die. Example 3 : Suppose a flashlight is left on until the battery runs out. Then we could define the random variable Z to represent the amount of time that passed. Types of Random Variables 1. A finite discrete random variable is one which can only take on a limited number of values that can be listed. 2. An infinite discrete random variable is one which can take on an unlimited number of values that can be listed in some sort of sequence. 3. A continuous random variable is one which takes on any of the infinite number of values in some interval
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Unformatted text preview: of real numbers. (i.e. usually measurements) Example 4 : Referring to Example 1, find the probability distribution of the random variable X . 1 c ± Kendra Kilmer October 27, 2011 Example 5 : The number of cars waiting in line at the beginning of 2-minute intervals at a certain bank was observed. The following data was collected: Number of cars 1 2 3 4 Frequency of occurence 2 2 16 8 2 Let X represent the number of cars observed waiting in line and find the probability distribution of X We use histograms to represent the probability distributions of random variables. We place the possible values for the random variable X on the horizontal axis. We then center a bar around each x value and let its height be equal to the probability of that x value. Example 6 : Referring to Example 5, a) Draw the histogram for the random variable X b) Find P ( X ≥ 2 ) Section 8.1 Highly Suggested Homework Problems: 1, 5, 7, 9, 19, 21, 23, 25 2...
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