Chapter4.34

# Chapter4.34 - 4.3 Random Variables Key Words in Section 4.3...

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4.3 Random Variables Key Words in Section 4.3 Random Variable: Discrete random variable Continuous random variable Random variable A random variable is a function that takes each possible outcome in the sample space and maps it into a numeric value. For example define the random variable X as the number of heads in 2 tosses of a fair, 50-50 coin. The sample space is } , , , { TT TH HH HT S = the corresponding outcomes in this sample space get associated with values of the random variable X as } 0 , 1 , 2 , 1 { because the outcomes have 1,2,1, and 0 heads respectively.

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Discrete Random variable A discrete random variable X has a finite number of possible values. The probability distribution of X lists the values and their probabilities: Value of X Probability X 1 p 1 X 2 p 2 X 3 p 3 : : : : X k p k The Probabilities p i must satisfy two requirements: 1. Every probability p i is a number between 0 and 1. 2. p 1 +p 2 +p k = 1 We usually summarize all the information about a random variable with a probability table like: X 0 1 2 ------------------------------------ P(x) 1/4 1/2 1/4 this is the probability table representing the random variable X defined above for the 2 toss
coin tossing experiment. There is one outcome with zero heads, 2 with one head, and one with 2 heads. All outcomes are equally likely, and this means the probabilities are defined as the number of outcomes in the event divided by the total number of outcomes. See the text for other random variable examples. The text draws the random variable tables horizontally across the page, but this doesn't matter.

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Figure 4.5 Probability histograms for (a) random digits 1 to 9 and (b) Benford’s Law. The height of each bar shows the probability assigned to a single outcome. The information in a probability table can also be
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Chapter4.34 - 4.3 Random Variables Key Words in Section 4.3...

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