6. Three points A, B, C are chosen independently at random on the circumference of a circle. Let b(x) be the probability that at least one of the angles of the triangle ABC exceeds xл. Show that - 1 − (3x − 1)² if ≤ x ≤ 1, if ≤ x ≤ 1. 3(1-x)² Hence find the density and expectation of the largest angle in the triangle. b(x) = {
6. Three points A, B, C are chosen independently at random on the circumference of a circle. Let b(x) be the probability that at least one of the angles of the triangle ABC exceeds xл. Show that - 1 − (3x − 1)² if ≤ x ≤ 1, if ≤ x ≤ 1. 3(1-x)² Hence find the density and expectation of the largest angle in the triangle. b(x) = {
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter6: The Trigonometric Functions
Section6.4: Values Of The Trigonometric Functions
Problem 24E
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Transcribed Image Text:6. Three points A, B, C are chosen independently at random on the circumference of a circle. Let
b(x) be the probability that at least one of the angles of the triangle ABC exceeds xл. Show that
-
1 − (3x − 1)² if ⁄ ≤ x ≤ 1,
if ≤ x ≤ 1.
3(1-x)²
Hence find the density and expectation of the largest angle in the triangle.
b(x) =
{
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