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Normal Probability Distribution The function f(x) = 1 글 O√√27 is called the normal probability density function with the mean and standard deviation o. The number tells where the distribution is centered, and o measures the "scatter" around the mean. From the theory of probability, it is known that [ f(x)dx=1. 88 In what follows, let u=0 and o=1. A) Draw the graph of f. Find the intervals on which the fis increasing, the intervals on which fis decreasing, and any local extreme values and where they occur.

Normal Probability Distribution The function f(x) = 1 글 O√√27 is called the normal probability density function with the mean and standard deviation o. The number tells where the distribution is centered, and o measures the "scatter" around the mean. From the theory of probability, it is known that [ f(x)dx=1. 88 In what follows, let u=0 and o=1. A) Draw the graph of f. Find the intervals on which the fis increasing, the intervals on which fis decreasing, and any local extreme values and where they occur.

College Algebra
College Algebra
10th Edition
ISBN:9781337282291
Author:Ron Larson
Publisher:Ron Larson
Chapter5: Exponential And Logarithmic Functions
Section5.5: Exponential And Logarithmic Models
Problem 4ECP
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Normal Probability Distribution The function f(x) = 1 2 (X-A² O√√2T is called the normal probability density function with the mean and standard deviation o. The number tells where the distribution is centered, and measures the "scatter" around the mean. From the theory of probability, it is known that [ f(x)dx=1. -00 In what follows, let u=0 and o=1. A) Draw the graph of f. Find the intervals on which the fis increasing, the intervals on which fis decreasing, and any local extreme values and where they occur.
Transcribed Image Text:Normal Probability Distribution The function f(x) = 1 2 (X-A² O√√2T is called the normal probability density function with the mean and standard deviation o. The number tells where the distribution is centered, and measures the "scatter" around the mean. From the theory of probability, it is known that [ f(x)dx=1. -00 In what follows, let u=0 and o=1. A) Draw the graph of f. Find the intervals on which the fis increasing, the intervals on which fis decreasing, and any local extreme values and where they occur.
B) Use your graphing calculator or an on-line CAS program to evaluate. In for n=1, 2 and 3. C) Give a convincing argument that U f(x)dx j f(x)dx=1 m Hint: Show that b 0< f(x) <e2 for x>1, and for b>1, Sex¹²2dx →0 as b→∞.
Transcribed Image Text:B) Use your graphing calculator or an on-line CAS program to evaluate. In for n=1, 2 and 3. C) Give a convincing argument that U f(x)dx j f(x)dx=1 m Hint: Show that b 0< f(x) <e2 for x>1, and for b>1, Sex¹²2dx →0 as b→∞.
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