Michael Corral: Vector Calculus

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130 CHAPTER 3. MULTIPLE INTEGRALS Example 3.16. A famous distribution function is given by the standard normal distribution, whose probability density function f is f(x)= 1 √ 2π e −x2 /2 , for−∞< x
3.7 Application: Probability and Expected Value 131 In addition to individual random variables, we can consider jointly distributed randomvariables. Forthis,wewilllet X,Y andZ bethreereal-valuedcontinuousrandom variables defined on the same sample spaceΩin(the discussion for two random variables is similar). Then the joint distribution function F of X, Y and Z is given by F(x,y,z)=P(X≤x, Y≤ y, Z≤ z), for−∞< x,y,z
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1 0.8 0.6 0.4 z 0.2 0 -0.2 -0.4 -10
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About the author: Michael Corral is
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iv Preface matter, anyone can make
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vi Contents 4.4 Surface Integrals a
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2 CHAPTER 1. VECTORS IN EUCLIDEAN S
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10 CHAPTER 1. VECTORS IN EUCLIDEAN
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66 CHAPTER 2. FUNCTIONS OF SEVERAL
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180 CHAPTER 4. LINE AND SURFACE INT
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188 Bibliography Pogorelov, A.V., A
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190 Appendix A: Answers and Hints t
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Appendix B We will prove the right-
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194 Appendix B: Proof of the Right-
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Appendix C 3D Graphing with Gnuplot
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198 Appendix C: 3D Graphing with Gn
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200 Appendix C: 3D Graphing with Gn
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202 GNU Free Documentation License
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Index Symbols D....................
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212 Index iterated integral .......
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Michael Corral: Vector Calculus

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