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Unformatted text preview: Y = X 2 where X is a continuous random variable with PDF shown above. Then Y is a continuous random variable with a range of (0,1). As we discussed earlier in the classroom, the CDF of Y carries the same amount of information as the PDF of Y . Let us ﬁrst evaluate the probability P [ Y ≤ . 5]. F Y (0 . 5) = P [ Y ≤ . 5] = P [ X 2 ≤ . 5] = P [ X ≤ √ . 5] = Z √ . 5∞ f ( x ) dx = Z √ . 5 1 dx = √ . 5 . We can replace 0 . 5 by a general y to get F Y ( y ) = √ y where 0 < y < 1. In summary, we have F Y ( y ) = y ≤ √ y < y < 1 1 y ≥ 1 . Taking the derivative of F Y ( y ) with respect to y , we obtain the PDF for Y , i.e., f Y ( y ) = 1 2 y1 / 2 < y < 1 elsewhere ....
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This note was uploaded on 01/19/2012 for the course IEN 311 taught by Professor Qiu during the Spring '11 term at University of Miami.
 Spring '11
 Qiu

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