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Probability and Statistics | 4th Edition | ISBN: 9780321500465 | Authors: Morris H. DeGroot, Mark J. Schervish
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Suppose that in a certain drug the concentration of a

Chapter 3, Problem 6

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QUESTION:

Suppose that in a certain drug the concentration of a particular chemical is a random variable with a continuous distribution for which the p.d.f. g is as follows: g(x) = 3 8 x2 for 0 x 2, 0 otherwise. Suppose that the concentrations X and Y of the chemical in two separate batches of the drug are independent random variables for each of which the p.d.f. is g. Determine (a)the joint p.d.f. ofX and Y ;(b)Pr(X = Y );(c)Pr(X > Y ); (d) Pr(X + Y 1

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QUESTION:

Suppose that in a certain drug the concentration of a particular chemical is a random variable with a continuous distribution for which the p.d.f. g is as follows: g(x) = 3 8 x2 for 0 x 2, 0 otherwise. Suppose that the concentrations X and Y of the chemical in two separate batches of the drug are independent random variables for each of which the p.d.f. is g. Determine (a)the joint p.d.f. ofX and Y ;(b)Pr(X = Y );(c)Pr(X > Y ); (d) Pr(X + Y 1

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Given  and  are independent

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