A continuous random variable Y has the pdf S4 y > 2 fy(y) = otherwise Let V = 1/vY. %3D (a) Show a sufficient amount of work to demonstrate that the cdf of Y is given by - {i- w>2 So y< 2 Fy(y) = (b) State the support of the random variable V (i.e. the set of all possible values of V). (c) Use the method of distribution functions to find the cdf of V, and then determine the pdf of V from your cdf. (d) Use the method of transformations to determine the pdf of V. (HINT: Your pdf should agree with that from above, so this can serve as a check on your work.)

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1. A continuous random variable Y has the pdf
器 y>2
fy (y) =
otherwise
Let V = 1/VY.
(a) Show a sufficient amount of work to demonstrate that the cdf of Y is given by
so
(1- y > 2
y < 2
Fy(y)
=
(b) State the support of the random variable V (i.e. the set of all possible values of V).
(c) Use the method of distribution functions to find the cdf of V, and then determine the pdf of V
from your cdf.
(d) Use the method of transformations to determine the pdf of V. (HINT: Your pdf should agree
with that from above, so this can serve as a check on your work.)
Transcribed Image Text:1. A continuous random variable Y has the pdf 器 y>2 fy (y) = otherwise Let V = 1/VY. (a) Show a sufficient amount of work to demonstrate that the cdf of Y is given by so (1- y > 2 y < 2 Fy(y) = (b) State the support of the random variable V (i.e. the set of all possible values of V). (c) Use the method of distribution functions to find the cdf of V, and then determine the pdf of V from your cdf. (d) Use the method of transformations to determine the pdf of V. (HINT: Your pdf should agree with that from above, so this can serve as a check on your work.)
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