Let C1 be the disk with its center at the origin in the xy-plane and radius 1. Calculate P((X, Y ) ∈ C1) which is the probability that a point (X, Y ) lies in the region C1.
Let C1 be the disk with its center at the origin in the xy-plane and radius 1. Calculate P((X, Y ) ∈ C1) which is the probability that a point (X, Y ) lies in the region C1.
A First Course in Probability (10th Edition)
10th Edition
ISBN:9780134753119
Author:Sheldon Ross
Publisher:Sheldon Ross
Chapter1: Combinatorial Analysis
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Let C1 be the disk with its center at the origin in the xy-plane and radius 1. Calculate P((X, Y ) ∈ C1) which is the
Transcribed Image Text:Thus, the function
has the following properties:
f (x, y)
=
1-(x²+y²)
ㅠ
f(x, y) ≥0 and [[ f(x,y) dA = 1.
Since f satisfies these two properties, f is called a joint density function. So, f can be used
to define the probability that a point (X, Y) lies in a region D, denoted as P((X, Y) € D), in
the following way:
P((X, Y) € D) := √√ ƒ (x,y) dA.
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