A sharpshooter is aiming at a circular target withradius 1. If we draw a rectangular system of coordinates with its origin at the center of the target, the coordinates of the point of impact, (X, Y), are random variables hav-ing the joint probability density f(x, y) =⎧⎪⎪⎨⎪⎪⎩1π for 0 < x2 + y2 < 10 elsewhere Find(a) P[(X, Y) ∈ A], where A is the sector of the circle inthe first quadrant bounded by the lines y = 0 and y = x;(b) P[(X, Y) ∈ B], where B = {(x, y)|0 < x2 + y2 < 12
A sharpshooter is aiming at a circular target withradius 1. If we draw a rectangular system of coordinates with its origin at the center of the target, the coordinates of the point of impact, (X, Y), are random variables hav-ing the joint probability density f(x, y) =⎧⎪⎪⎨⎪⎪⎩1π for 0 < x2 + y2 < 10 elsewhere Find(a) P[(X, Y) ∈ A], where A is the sector of the circle inthe first quadrant bounded by the lines y = 0 and y = x;(b) P[(X, Y) ∈ B], where B = {(x, y)|0 < x2 + y2 < 12
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
Related questions
Question
A sharpshooter is aiming at a circular target with
radius 1. If we draw a rectangular system of coordinates
with its origin at the center of the target, the coordinates
of the point of impact, (X, Y), are random variables hav-
ing the joint probability density
ing the joint probability density
f(x, y) =
⎧
⎪⎪⎨
⎪⎪⎩
1
π for 0 < x2 + y2 < 1
0 elsewhere
⎧
⎪⎪⎨
⎪⎪⎩
1
π for 0 < x2 + y2 < 1
0 elsewhere
Find
(a) P[(X, Y) ∈ A], where A is the sector of the circle in
the first quadrant bounded by the lines y = 0 and y = x;
(b) P[(X, Y) ∈ B], where B = {(x, y)|0 < x2 + y2 < 1
2
(a) P[(X, Y) ∈ A], where A is the sector of the circle in
the first quadrant bounded by the lines y = 0 and y = x;
(b) P[(X, Y) ∈ B], where B = {(x, y)|0 < x2 + y2 < 1
2
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