Characteristic function of Laplace distribution: Why can't c equal -sqrt(p)?

[Nox]

The first screenshot is the question and the second is the answer.

In part (b) why can't c equal -sqrt(p)? if I insert -sqrt(p) in the characteristic function of Y I still get [imath]\frac{1}{1 + a^2t^2}[/imath] which gives Y∈L(a)


solution:

 

[khansaheb]

The first screenshot is the question and the second is the answer.

In part (b) why can't c equal -sqrt(p)? if I insert -sqrt(p) in the characteristic function of Y I still get [imath]\frac{1}{1 + a^2t^2}[/imath] which gives Y∈L(a)View attachment 36528


solution:
View attachment 36529

Read the last paragraph carefully (preferably using pencil/paper and your textbook).
What is the definition of:

permitted Laplace distribution?​

 

[Nox]

Read the last paragraph carefully (preferably using pencil/paper and your textbook).
What is the definition of:

permitted Laplace distribution?​

I see, I get Y∈L(-a) if I use c=-sqrt(p)

Thank you for the help : )