Explanation Given Information: The provided table is, x 0 1 2 3 4 5 6 7 s ( x ) 1 5 1 s ¯ ( x ) 5 5 2 3 2 Formula used: For any natural number m, the average of m numbers is, b 1 + b 2 + ..... + b m m , where each number is denoted by b i ( i = 1 , 2 , ..... , m ) . The n-unit moving average of a function s ( x ) is, for each x , the average of values of s ( x ) together with the values of s ( x ) for the previous n − 1 values of x . That is, the n -unit moving average of a function s ( x ) for x = x t is, s ¯ ( x t ) = s ( x t ) + s ( x t − 1 ) + … + s ( x t − ( n − 1 ) ) n . Calculation: Consider the table, x 0 1 2 3 4 5 6 7 s ( x ) 1 5 1 s ¯ ( x ) 5 5 2 3 2 Let x i denote the values of x for 1 ≤ i ≤ 8 . That is, x 1 = 0 , x 2 = 1 , x 3 = 2 , x 4 = 3 , and x 5 = 4 , x 6 = 5 , x 7 = 6 , x 8 = 7 . The provided values of function are, s ( x 1 ) = 1 , s ( x 2 ) = 5 , s ( x 4 ) = 1 and the provided values of its 3-unit moving average is s ¯ ( x 3 ) = 5 , s ¯ ( x 5 ) = 5 , s ¯ ( x 6 ) = 2 , s ¯ ( x 7 ) = 3 , s ¯ ( x 8 ) = 2 . Recall that, the n -unit moving average of a function s ( x ) is, for each x , the average of values of s ( x ) together with the values of s ( x ) for the previous n − 1 values of x . That is, the n -unit moving average of a function s ( x ) for x = x t is, s ¯ ( x t ) = s ( x t ) + s ( x t − 1 ) + … + s ( x t − ( n − 1 ) ) n . The provided value of n is 3. Consider x = x 3 . Substitute 3 for t in s ¯ ( x t ) = s ( x t ) + s ( x t − 1 ) + … + s ( x t − ( n − 1 ) ) n . s ¯ ( x 3 ) = s ( x 3 ) + s ( x 2 ) + s ( x 1 ) 3 5 = s ( x 3 ) + 5 + 1 3 5 = s ( x 3 ) + 6 3 Multiply both sides by 3. 5 ⋅ 3 = s ( x 3 ) + 6 3 ⋅ 3 15 = s ( x 3 ) + 6 15 − 6 = s ( x 3 ) s ( x 3 ) = 9 Thus, s ( x 3 ) = 9 . Consider x = x 4 . Substitute 4 for t in s ¯ ( x t ) = s ( x t ) + s ( x t − 1 ) + … + s ( x t − ( n − 1 ) ) n . s ¯ ( x 4 ) = s ( x 4 ) + s ( x 3 ) + s ( x 2 ) 3 = 1 + 9 + 5 3 = 15 3 = 5 Thus, s ¯ ( x 4 ) = 5 . Consider x = x 5

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ISBN: 9781337291248

Author: Waner, Stefan.

Publisher: Cengage Learning,

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In simple mathematics terms, a domain is defined as the space on which all the possible inputs for the function will lie. It can also be expressed as a set of departures for the required function.

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Chapter 7.3, Problem 12E

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To calculate: The missing values of the function s(x) and its 3-unit moving average from the table.

x 0 1 2 3 4 5 6 7

s(x) 1 5 1

s¯(x) 5 5 2 3 2

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Chapter 7.3, Problem 11E

Chapter 7.3, Problem 13E

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The missing values of the function s ( x ) and its 3-unit moving average from the table. x 0 1 2 3 4 5 6 7 s ( x ) 1 5 1 s ¯ ( x ) 5 5 2 3 2

Solution Summary: The author calculates the missing values of the function s(x) and its 3-unit moving average from the table.

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To calculate: The missing values of the function s(x) and its 3-unit moving average from the table.

x 0 1 2 3 4 5 6 7

s(x) 1 5 1

s¯(x) 5 5 2 3 2

Want to see the full answer?

Chapter 7 Solutions

The missing values of the function s ( x ) and its 3-unit moving average from the table. x 0 1 2 3 4 5 6 7 s ( x ) 1 5 1 s ¯ ( x ) 5 5 2 3 2

Solution Summary: The author calculates the missing values of the function s(x) and its 3-unit moving average from the table.

Concept explainers

Videos

To calculate: The missing values of the function s(x) and its 3-unit moving average from the table. x 0 1 2 3 4 5 6 7 s(x) 1 5 1 s¯(x) 5 5 2 3 2

Want to see the full answer?

Chapter 7 Solutions

To calculate: The missing values of the function s(x) and its 3-unit moving average from the table.

x 0 1 2 3 4 5 6 7

s(x) 1 5 1

s¯(x) 5 5 2 3 2