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Let (X, Y) be a random point in the unit square, [0, 1] x [0, 1], with the uniform probability. That is, X is a random number between 0 and 1, and Y is a random number between 0 and 1. overall task is to compute P(X < (3/4) given Y < (1/2)X). Draw the Cartesian plane (make sure there is plenty of room in the first quadrant), and draw and label the axes. Sketch the sample space, [0, 1] x [0, 1], in the first quadrant. = Draw the graph of the line Y (1/2) X in the sample space. Label the points where this line intersects the corners or sides of the unit square. Compute P(Y < (1/2)X) by finding the area of the triangular region underneath the line Y (12) x and dividing by the area of the sample space.

Let (X, Y) be a random point in the unit square, [0, 1] x [0, 1], with the uniform probability. That is, X is a random number between 0 and 1, and Y is a random number between 0 and 1. overall task is to compute P(X < (3/4) given Y < (1/2)X). Draw the Cartesian plane (make sure there is plenty of room in the first quadrant), and draw and label the axes. Sketch the sample space, [0, 1] x [0, 1], in the first quadrant. = Draw the graph of the line Y (1/2) X in the sample space. Label the points where this line intersects the corners or sides of the unit square. Compute P(Y < (1/2)X) by finding the area of the triangular region underneath the line Y (12) x and dividing by the area of the sample space.

MATLAB: An Introduction with Applications
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
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Need help with unit square. Probability.

Let (X, Y) be a random point in the unit square, [0, 1] × [0, 1], with the uniform probability. That is, X is a random number between 0 and 1, and Y is a random number between 0 and 1. overall task: is to compute P (X < (3/4) given Y < (1/2)X). Draw the Cartesian plane (make sure there is plenty of room in the first quadrant), and draw and label the axes. Sketch the sample space, [0, 1] × [0, 1], in the first quadrant. = Draw the graph of the line Y (1/2)X in the sample space. Label the points where this line intersects the corners or sides of the unit square. Compute P(Y < (1/2)X) by finding the area of the triangular region underneath the line Y = (1/2) × and dividing by the area of the sample space.
Transcribed Image Text:Let (X, Y) be a random point in the unit square, [0, 1] × [0, 1], with the uniform probability. That is, X is a random number between 0 and 1, and Y is a random number between 0 and 1. overall task: is to compute P (X < (3/4) given Y < (1/2)X). Draw the Cartesian plane (make sure there is plenty of room in the first quadrant), and draw and label the axes. Sketch the sample space, [0, 1] × [0, 1], in the first quadrant. = Draw the graph of the line Y (1/2)X in the sample space. Label the points where this line intersects the corners or sides of the unit square. Compute P(Y < (1/2)X) by finding the area of the triangular region underneath the line Y = (1/2) × and dividing by the area of the sample space.
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