Explanation Formula used: Normal probability density function : The function is, f ( x ) = 1 σ 2 π e − ( x − μ ) 2 / 2 σ 2 , σ ≥ 0 . The median of normal probability density function is μ . Uniform probability density function : The function is, f ( x ) = { 1 b − a if a ≤ x ≤ b 0 otherwise . The median of uniform probability function is, m = 1 2 ( a + b ) . Calculation: The probability density functions are f 1 ( x ) = 1 2 π e − x 2 / 2 and f 2 ( x ) = { 0 .4 if − 1.25 ≤ x ≤ 1.25 0 otherwise . Draw the graph of the functions f 1 ( x ) and f 2 ( x ) as shown below in Figure 1. From Figure 1, it is observed that the graph of both the probability density functions f 1 ( x ) and f 2 ( x ) are symmetric with respect to the line x = 0 . Here, the median value is 0 for both the functions. The probability density function f 1 ( x ) = 1 2 π e − x 2 / 2 represents a standard normal distribution

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Chapter 11.4, Problem 34E

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To explain: The medians of the probability density functions from the graph of f1(x) and f2(x).

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Chapter 11.4, Problem 33E

Chapter 11.4, Problem 35E

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Chapter 11 Solutions

EBK CALCULUS FOR BUSINESS, ECONOMICS, L

Ch. 11.1 - Evaluate the following, if it converges: 3dx(x1)2.Ch. 11.1 - Prob. 2MP Ch. 11.1 - Prob. 3MP Ch. 11.1 - Prob. 4MP Ch. 11.1 - Prob. 5MP Ch. 11.1 - Prob. 6MP Ch. 11.1 - Prob. 1ED Ch. 11.1 - Prob. 2ED Ch. 11.1 - Prob. 1E Ch. 11.1 - Prob. 2E

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The medians of the probability density functions from the graph of f 1 ( x ) and f 2 ( x ) .

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