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Probability Theory and Statistics Exercise 11 1. Suppose that the p.dforisf(x)-F ,x> , where σ is constant. Find the value of ELX) and Dr. 2. Suppose that the p.dfof (x.r is (x,y)- 1Sxy, 0SysI Find the value of D) 0 otherwise and D(). 3. Suppose that of x- - N(0.0.5), Y N(00.5) and .X.Y are independent. Determine the variance
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Answer #1

Take. E(X) = 0 252 17 448

3, Var(Y-Y Since X and Y are independent so X - YN(0,1) Hence E(X-Y)2-Var(X-Y)-1, since E(X-Y) = 0 π-2 Hence Var(X-Y) = 1--=

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