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Example 6-19. From a point on the circumference of a circle of radius 'a', a chort drawn in a random direction, (all directions being equally likely). Show that the expected of the length of the chord is 4a/t and that the variance of the length is 2a² (1 - 3) 8. Also show that the length of the chord will excecd the length of the side of an that the chance is equilateral triangle inscribed in the circle.

Example 6-19. From a point on the circumference of a circle of radius 'a', a chort drawn in a random direction, (all directions being equally likely). Show that the expected of the length of the chord is 4a/t and that the variance of the length is 2a² (1 - 3) 8. Also show that the length of the chord will excecd the length of the side of an that the chance is equilateral triangle inscribed in the circle.

Algebra & Trigonometry with Analytic Geometry
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter10: Sequences, Series, And Probability
Section10.8: Probability
Problem 32E
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drawn in a random direction, (all directions being equally likely). Show that the expected value Example 6-19. From a point on the circumference of a circle of radius 'a', a chord drozon in a random direction, (all directions being equally likely). Show that the expected natue 8. of the length of the chord is 4a/T and that the variance of the length is 2a² ( 1 – º ) Alco de that the chance is that the length of the chord will exceed the length of the side of a equilateral triangle inscribed in the circle.
Transcribed Image Text:drawn in a random direction, (all directions being equally likely). Show that the expected value Example 6-19. From a point on the circumference of a circle of radius 'a', a chord drozon in a random direction, (all directions being equally likely). Show that the expected natue 8. of the length of the chord is 4a/T and that the variance of the length is 2a² ( 1 – º ) Alco de that the chance is that the length of the chord will exceed the length of the side of a equilateral triangle inscribed in the circle.
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