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Unformatted text preview: ). ( y f Y (b) X ∼ ) , ( 2 σ N ( X is a normal r.v with parameters 0 and 2 ). (i) Define . 2 X Y = Find ). ( y F Y (ii) Define .   X Z = Find ). ( z f Z 2 6. (a) Let X be the r.v with p.d.f ∞ < < ≤ < ≤ = . 1 , 2 / 1 , 1 , 2 / 1 , , ) ( 2 x x x x x f X Find the p.d.f of the r.v . / 1 X Z = (b) X is given to be uniform in ( 29 . , πDefine . sec X Y = Compute ). ( y f Y 7. (a) Define the event M as ( 29 ( 29 . 2 1 ≤ < ∪ ≤ = X X M Find )  ( M x F X and )  ( M x f X in terms of ) ( x F X and ) ( x f X where X is a nonzero r.v over the entire real axis. (b) Let X be a r.v with p.d.f given by < < = . , , , / 2 ) ( 2 elsewhere x x x f X Define . sin X Y = Find the p.d.f of the r.v Y ....
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 Spring '11
 voltz
 Probability theory, Discrete probability distribution, Probability mass function, R.V

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