A sharpshooter is aiming at a circular target with radius 1. If we draw a rectangular system
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 having the joint probability density
Find
(a) P[(X,Y) ϵ A], where A is the sector of the circle in the first quadrant bounded by the lines y = 0 and y = x;
for 0 y <1 0 elsewhere
Step by Step Answer:
a Prob...View the full answer
John E Freunds Mathematical Statistics With Applications
ISBN: 9780134995373
8th Edition
Authors: Irwin Miller, Marylees Miller
Related Video
The area of a circle is given by the formula: A = ?r^2 Where A is the area, ? is a mathematical constant (approximately 3.14), and r is the radius of the circle. The radius is the distance from the center of the circle to the edge. So for example, if the radius of a circle is 5 units, the area would be: A = ?(5^2) = ?(25) = 78.5 square units Here three friends went out to a restaurant and decided to have pizza for lunch. While they were waiting for their order, one of them stepped out to take a call but promised to return in two minutes. The waiter came and presented them with the menu, and they decided to order two 10-inch pepperoni pizzas. The waiter took their order and left. Just then, the third friend returned and asked what they had ordered. They explained that they had ordered two small pepperoni pizzas as they were only three of them and it would be enough for them. However, the third friend suggested that for the same price, they could get a large pizza that would be much bigger than the two small ones. He asked the waiter for a pen and paper and proceeded to calculate the area of the two small pizzas and compared it to the area of one large pizza. The friends were amazed at how the circle measurements worked and decided to change their order from two small pizzas to one large pizza.
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