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Give a convincing argument that f(x)dx=1

Give a convincing argument that f(x)dx=1

Calculus For The Life Sciences
Calculus For The Life Sciences
2nd Edition
ISBN:9780321964038
Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Publisher:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Chapter3: The Derivative
Section3.4: Definition Of The Derivative
Problem 3E
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I need part C. It has to show that the integral from -infinity to -b and the integral from infinity to b equal 0 and the integral of -b to b equals 1 to prove the question. Please show all work!!!!
j -n f (x)dx for n= 1, 2 and 3. C) Give a convincing argument that | f(x)dx=1 Hint: Show that 0<f(x) <e2 for x>1, and for b>1, je vzdx. -x/2dx0 as b→∞.
Transcribed Image Text:j -n f (x)dx for n= 1, 2 and 3. C) Give a convincing argument that | f(x)dx=1 Hint: Show that 0<f(x) <e2 for x>1, and for b>1, je vzdx. -x/2dx0 as b→∞.
Normal Probability Distribution The function 1 (² O√√2T f(x) = - 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. In what follows, let μ = 0 and o=1.
Transcribed Image Text:Normal Probability Distribution The function 1 (² O√√2T f(x) = - 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. In what follows, let μ = 0 and o=1.
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