Probability: Determining the distribution and range of a random variable

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Homework Statement



The RV X has parameter p>0 and distribution:

fX(x) = pxe-px for x [tex]\geq[/tex] 0 and is 0 otherwise

(The subscript X is a capital letter, as is the X mentioned below in the e4X)

If we are to consider the RV D= e4X, determine the range and distribution fD(d)


Homework Equations





The Attempt at a Solution



I found this question as an exercise in a textbook, but do not know how to answer it!
Does anyone have any suggestions that I can try out please?
 

Answers and Replies

  • #2
LCKurtz
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Start by figuring out what p must be for fX to be a density function.

If D = e4X, one way to get at its density function is to use the cumulative distribution:

P(D ≤ d) = P(e4X ≤ d) = P(4X ≤ ln(d)) = P( X ≤ (1/4)ln(d) )

Presumably you can calculate that, which will give you the cumulative distribution function for D. Differentiate to get fD(d).
 

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