Consider the triangle A on R2 formed by three points: (0,0), (1,0), and P, where P has coordinates (cos, sin ), with uniformly chosen from [0, 2π] (i.e., ~ uniform([0, 27])). (Note that P is on the unit circle x² + y² = 1). (a) Find the probability that A is an obtuse triangle. (b) Find the probability that A has area ≤ 1. (c) Let A be the area of A. Find E[A], Var[A].
Consider the triangle A on R2 formed by three points: (0,0), (1,0), and P, where P has coordinates (cos, sin ), with uniformly chosen from [0, 2π] (i.e., ~ uniform([0, 27])). (Note that P is on the unit circle x² + y² = 1). (a) Find the probability that A is an obtuse triangle. (b) Find the probability that A has area ≤ 1. (c) Let A be the area of A. Find E[A], Var[A].
A First Course in Probability (10th Edition)
10th Edition
ISBN:9780134753119
Author:Sheldon Ross
Publisher:Sheldon Ross
Chapter1: Combinatorial Analysis
Section: Chapter Questions
Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...
Related questions
Question
![Consider the triangle A on R2 formed by three points: (0,0), (1,0), and
P, where P has coordinates (cos, sin Ⓒ), with uniformly chosen from [0, 2π] (i.e.,
uniform([0, 2π])). (Note that P is on the unit circle x² + y² = 1).
(a) Find the probability that A is an obtuse triangle.
(b) Find the probability that A has area ≤
(c) Let A be the area of A. Find E[A], Var[A].](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fd94c6fe5-0a79-4b34-8240-29323f6fd175%2F822eb218-1d06-4ef7-a115-81bddc719b28%2F9xt4oep_processed.jpeg&w=3840&q=75)
Transcribed Image Text:Consider the triangle A on R2 formed by three points: (0,0), (1,0), and
P, where P has coordinates (cos, sin Ⓒ), with uniformly chosen from [0, 2π] (i.e.,
uniform([0, 2π])). (Note that P is on the unit circle x² + y² = 1).
(a) Find the probability that A is an obtuse triangle.
(b) Find the probability that A has area ≤
(c) Let A be the area of A. Find E[A], Var[A].
Expert Solution
This question has been solved!
Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.
Step by step
Solved in 2 steps with 1 images
Recommended textbooks for you
A First Course in Probability (10th Edition)
Probability
ISBN:
9780134753119
Author:
Sheldon Ross
Publisher:
PEARSON
A First Course in Probability (10th Edition)
Probability
ISBN:
9780134753119
Author:
Sheldon Ross
Publisher:
PEARSON