3. The normal curve (or the Gaussian), defined as g(x)plays an important role in probability andV27+oostatistics. It is useful to know that| g(x) dx = 1, which we will now show.-00(a) Suppose that Da is a disk, centered at the origin, with radius a. Explain why+ooe-(z²+y³)/2dx dylime-(a²+y²)/2dA.(b) Change to polar coordinates to evaluatee-(a2+y²)/2 dA, and take the limit as a → +o.Da(c) Explain whytoo+oo+ootoo"|e-=²+s²)/2 dA =x² /2 dx-y²/2dy-00-00(d) Conclude that|e-a*/2 dx = V27, so thatdx = 1, aswe hoped.

A coordinate system is a convention that is used to represent a point uniquely using a set of…

. The normal curve (or the Gaussian), defined as g(x) = 27 plays an important role in probability and statistics. It is useful to know that | g(x) dx = 1, which we will now show. (a) Suppose that Da is a disk, centered at the origin, with radius a. Explain why *e-*+v*)/2 dr dy = lim // e-(z²+u*)/2 dA. (b) Change to polar coordinates to evaluate || e-(x²+y²)/2 dA, and take the limit as a –→+∞. (c) Explain why +oo e-(2²+y³)/2 dA = 1² /2 dx e-v³/2 dy e -00 (d) Conclude that e-2* /2 dx = V27, so that g(x) dx = 1, as we hoped.

. The normal curve (or the Gaussian), defined as g(x) = 27 plays an important role in probability and statistics. It is useful to know that | g(x) dx = 1, which we will now show. (a) Suppose that Da is a disk, centered at the origin, with radius a. Explain why e-+v)/2 dr dy = lim // e-(z²+u)/2 dA. (b) Change to polar coordinates to evaluate || e-(x²+y²)/2 dA, and take the limit as a –→+∞. (c) Explain why +oo e-(2²+y³)/2 dA = 1² /2 dx e-v³/2 dy e -00 (d) Conclude that e-2* /2 dx = V27, so that g(x) dx = 1, as we hoped.

Algebra & Trigonometry with Analytic Geometry

13th Edition

ISBN:9781133382119

Author:Swokowski

Publisher:Swokowski

Chapter7: Analytic Trigonometry

Section7.6: The Inverse Trigonometric Functions

Problem 91E

See similar textbooks