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1.11 The solutions of the differential equation dy a - x dx B+ yx + dx² give most of the important distributions of statistics for appropriate choices of the constants a, B, and 8. Solve this differential equation when (1) a = 3 = 8 = 0, y > 0 (exponential distribution), (2) y = 8 = 0, B > 0 (normal distribution), (3) B = 8 = 0, y > 0, a > -y (gamma distribution), (4) B = 0, y= –d, (a – 1)/y < 1, a/y> -1 (beta distribution). %3D %3| %3D

1.11 The solutions of the differential equation dy a - x dx B+ yx + dx² give most of the important distributions of statistics for appropriate choices of the constants a, B, and 8. Solve this differential equation when (1) a = 3 = 8 = 0, y > 0 (exponential distribution), (2) y = 8 = 0, B > 0 (normal distribution), (3) B = 8 = 0, y > 0, a > -y (gamma distribution), (4) B = 0, y= –d, (a – 1)/y < 1, a/y> -1 (beta distribution). %3D %3| %3D

Calculus: Early Transcendentals
Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
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1.11 The solutions of the differential equation dy a - x dx B+ yx + 8x2 give most of the important distributions of statistics for appropriate choices of the constants a, B, y and 8. Solve this differential equation when (1) a = B = 8 = 0, y > 0 (exponential distribution), (2) y = 8 = 0, ß > 0 (normal distribution), (3) B = 6 = 0, y > 0, a > -y (gamma distribution), (4) B = 0, y = -8, (a – 1)/y < 1, a/y > -1 (beta distribution).
Transcribed Image Text:1.11 The solutions of the differential equation dy a - x dx B+ yx + 8x2 give most of the important distributions of statistics for appropriate choices of the constants a, B, y and 8. Solve this differential equation when (1) a = B = 8 = 0, y > 0 (exponential distribution), (2) y = 8 = 0, ß > 0 (normal distribution), (3) B = 6 = 0, y > 0, a > -y (gamma distribution), (4) B = 0, y = -8, (a – 1)/y < 1, a/y > -1 (beta distribution).
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