1313_section8o1

1313_section8o1 - 2 Example 1: Let X be the sum of the...

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Section 8.1 – Distributions of Random Variables 1 Section 8.1 Distributions of Random Variables A rule that assigns a number to each outcome of an experiment is called a random variable. Capital letters are often used to represent random variables. For example, a random variable X can represent the sum of the face values of two six- sided dice. The random variable may take on any number in the set {2, 3, …, 12}. We can construct the probability distribution associated with a random variable. If x 1 , x 2 , x 3 ,…, x n are values assumed by the random variable X with associated probabilities P ( X= x 1 ) = p 1 , P ( X= x 2 ) = p 2 , …, P ( X= x n ) = p n , respectively, then the probability distribution of X may be expressed in the following way. x P ( X = x ) x 1 p 1 x 2 p 2 . . . . . . x n p n We can also graphically represent the probability distribution of a random variable. A bar graph which represents the probability distribution of a random variable is called a histogram .
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Section 8.1 – Distributions of Random Variables
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Unformatted text preview: 2 Example 1: Let X be the sum of the faces of two dice. Probability distribution: x 2 3 4 5 6 7 8 9 10 11 12 ) ( x X P = 1/36 2/36 3/36 4/36 5/36 6/36 5/36 4/36 3/36 2/36 1/36 Evaluate the following using the histogram. a) ) 8 ( = X P b) ) 8 or 6 ( = = X X P c) ) 10 5 ( X P d) ) 9 ( X P Section 8.1 Distributions of Random Variables 3 Example 2: The rates paid by 30 financial institutions on a certain day for money-market deposit accounts are shown in the accompanying table: Rate, % 6 6.25 6.55 6.56 6.58 6.60 6.65 6.85 Number of Institutions 1 7 7 1 1 8 3 2 a. Let the random variable X denote the interest paid by a randomly chosen financial institution on its money-market deposit accounts and find the probability distribution associated with these data. b. Draw the histogram associated with these data. c. Find: P(6.55 < X < 6.58) P(X > 6.25)...
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1313_section8o1 - 2 Example 1: Let X be the sum of the...

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