Let X and Y denote random variables denoting the proportion of contaminants of type A and...
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Let X and Y denote random variables denoting the proportion of contaminants of type A and the proportion of contaminants of type B present in a landfill, respectively. A student calculated the conditional density function 2(x +y) f(y|x) = 0 < y < x, 3x2 and the marginal density function f(x) = 3x², 0 <x <1 (a) Calculate the join density of X and Y, and indicate the domain. (b) Calculate the Var(3X+Y). (c) Would you invoke the Central Limit theorem to calculate P(X +Y > 0.8)? Why or why not? Let X and Y denote random variables denoting the proportion of contaminants of type A and the proportion of contaminants of type B present in a landfill, respectively. A student calculated the conditional density function 2(x +y) f(y|x) = 0 < y < x, 3x2 and the marginal density function f(x) = 3x², 0 <x <1 (a) Calculate the join density of X and Y, and indicate the domain. (b) Calculate the Var(3X+Y). (c) Would you invoke the Central Limit theorem to calculate P(X +Y > 0.8)? Why or why not?
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Related Book For
Probability and Stochastic Processes A Friendly Introduction for Electrical and Computer Engineers
ISBN: 978-1118324561
3rd edition
Authors: Roy D. Yates, David J. Goodman
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