人工知能を使用せず、すべてを段階的にデジタル形式で解決してください。ありがとうSOLVE STEP BY STEP IN DIGITAL FORMATDON'T USE CHATGPT17. A function f(x, y) continuous in a region of the plane D will be called a density functionof probability if f(x, y) ≧ 0 for all (x, y) EDandJpf(x,y)=1.f(x,y)=a1+x² + y²Find the value of a so that the functionbe a density function of probability on the disk 0 ≤r ≤1000.

A function f(x,y) vover a region D is density function if f(x,y)≥0 and ∬Df(x,y)dA=1.Evaluating the…

Answered: 17. A function f(x, y) continuous in a…

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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We call p(x, y) the probability density function for attributes x and y if the probabilitythat an arbitrary member of a population has attribute x over the interval (a, b) as wellas attribute y over the interval (c, d), corresponds to the volume under the graph ofp(x, y) over the rectangle a ≤ x ≤ b, c ≤ y ≤ d, where the total volume under p(x, y)over the entire xy-plane is equal to 1 and p(x, y) ≥ 0 for all x and y. (a) Explain why the two conditions given at the end: “the total volumeunder p(x, y) over the entire xy-plane is equal to 1 and p(x, y) ≥ 0 for all x and y”are essential in the context of probabilities. Explain in simple terms (b) Express the probability (volume) referred to in the statement above as adouble integral. Intervals should correspond to the regionof integration and the order of integration are consistent and clearly indicated.(c) Use answer in part (b) withp(x, y) = (see image) to find 1. Verify that p(x, y) satisfies the definition (given above) of a…
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17. A function f(x, y) continuous in a region of the plane D will be called a density function of probability if f(x, y) ≥ 0 for all (x, y) E D and ₁ f(x,y) dA= 1. f(x,y)= a 1+z²+ Find the value of a so that the function be a density function of probability on the disk 0 ≤ r ≤1000.