Answered step by step
Verified Expert Solution
Question
1 Approved Answer
oblem 12. (12.4/36) (a) We define the improper integral (over the entire plane R2) 1= fferty'dA = [ ] effy dydr = lim ffe (fry
oblem 12. (12.4/36) (a) We define the improper integral (over the entire plane R2) 1= fferty'dA = [ ] effy dydr = lim ffe (fry da R- Da where Da is the disk with radius a and center the origin. Show that ( ( e (+7dydx=x. (b) An equivalent definition of the improper integral in part (a) is 1 = [e (+) dA = lim [fe-(+y)dA SA where Sa is the square with vertices (ta, ta) . Use this to show that ( ex dxf ey dy = 1 . -00 (c) Deduce that [ ex dx = n . (d) By making an appropriate change of variable, show that ( ex/2dx = 27 . [This is a fundamental result for probability and statistics, specifically the normal probability distribution.]
Step by Step Solution
There are 3 Steps involved in it
Step: 1
Get Instant Access to Expert-Tailored Solutions
See step-by-step solutions with expert insights and AI powered tools for academic success
Step: 2
Step: 3
Ace Your Homework with AI
Get the answers you need in no time with our AI-driven, step-by-step assistance
Get Started