Let Y = IXI, with X ,,, .Af(p,a2). This is a well-defined continuous r.v., even though the absolute value function is not differentiable at 0 (due to the sharp corner). (a) Find the CDF of Y in terms...

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Let Y = IXI, with X ,,, .Af(p,a2). This is a well-defined continuous r.v., even though the absolute value function is not differentiable at 0 (due to the sharp corner). (a) Find the CDF of Y in terms of (D. Be sure to specify the CDF everywhere. (b) Find the PDF of Y. (c) Is the PDF of Y continuous at 0? If not, is this a problem as far as using the PDF to find probabilities?

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Answered Same DayDec 26, 2021

Answer To: Let Y = IXI, with X ,,, .Af(p,a2). This is a well-defined continuous r.v., even though the absolute...

David answered on Dec 26 2021

130 Votes

Ans. 1
The given function,
2, ( , )y X X N  
So,
( ) ( ) ( ) ( ) ( ) ( )YF y P Y y P X y P y X y y y           
Apply the symmetry Principle,
1 2 ( )y 
Now thesupport for ( , )X is   in the same way, for is (0,+ )Y X 
Consider the CDF as,
0 for y 0
(...

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Let Y = IXI, with X ,,, .Af(p,a2). This is a well-defined continuous r.v., even though the absolute value function is not differentiable at 0 (due to the sharp corner). (a) Find the CDF of Y in terms...

Answer To: Let Y = IXI, with X ,,, .Af(p,a2). This is a well-defined continuous r.v., even though the absolute...

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