Transcription of Chapter 4: Multiple Random Variables - ntpu
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Chapter 4: Multiple Random Variables - ntpu
Chapter 4: Multiple Random Variables1. Yunghsiang S. Han Graduate Institute of Communication Engineering, National Taipei University Taiwan E-mail: 1 Modified from the lecture notes by Prof. Mao-Ching Chiu Y. S. Han Multiple Random Variables 1. Vector Random Variables Consider the two dimensional Random variable X = (X, Y ). Find the regions of the planes corresponding to the events A = {X + Y 10}, B = {min(X, Y ) 5} and C = {X 2 + Y 2 100}. Graduate Institute of Communication Engineering, National Taipei University Y. S. Han Multiple Random Variables 2. Graduate Institute of Communication Engineering, National Taipei University Y. S. Han Multiple Random Variables 3. Let the n-dimensional Random variable X be X = (X1 , X2 , .. , Xn ) and Ak be a one dimensional event that involves Xk . Events with product form is defined as A = {X1 A1 } {X2 A2 } {Xn An }. P [A] = P [{X1 A1 } {X2 A2 } {Xn An }].. = P [X1 A1 , .. , Xn An ]. Some events may not be of product form. Graduate Institute of Communication Engineering, National Taipei University Y.
Y. S. Han Multiple Random Variables 1 4.1 Vector Random Variables Consider the two dimensional random variable X = (X,Y). Find the regions of the planes corresponding
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