# Thread: What does this distribution mean?

1. ## What does this distribution mean?

When it says:

the marginal distribution of Y is given by

1/Y ~ Exponential(lamda)

does that mean the distribution is written has:

1/(lamda)e^(-lamda)(y)

??

Edit: Nevermind i think my first thought process is wrong, i believe its:

(lamda)e^(-lamda)(1/y)

if im right.

2. ## Re: What does this distribution mean?

if the probability density function of is

Then it is easy to show that the probability density function of is

Note: The expected value of is may not exist / finite.

3. ## Re: What does this distribution mean?

Originally Posted by BGM
if the probability density function of is

Then it is easy to show that the probability density function of is

Note: The expected value of is may not exist / finite.
just wondering, how did you get the 1/y^2 in the second equation of the PDF of Y? I thought its basically like that without the 1/y^2 if you can explain that.

4. ## Re: What does this distribution mean?

Basically you can try the CDF approach or the Jacobian Transformation on pdf
with 1-to-1 transformation.

1. Consider

Since we can get the pdf by differentiating the CDF, we have

2. Since

we have the absolute value of the Jacobian determinant

and thus

5. ## Re: What does this distribution mean?

Thanks that makes sense.

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