Thread Subject:

Gaussian pdf

Hi,
I'm a beginner in Matlab. I wanted to plot pdf of random variable y which is funtion of x. f(y)=aX^3+b. X is Gaussian random variable with zero mean and unit variance. By simplification pdf of y was obtained as:
    pY(y)=1/(3a*[〖(y-b)/a〗^(2/3)]*√2pi) e^(-1/2 [(y-b)/a〗^(2/3)])
that is in usual case we plot pdf of a variable x. here x=(y-b)/a
This is a problem found in Proakis Digital communication textbook. #2.4

"Jyothy MJ" <jyothymj@gmail.com> wrote in message <i7j2op$3q$1@fred.mathworks.com>...
> Hi,
> I'm a beginner in Matlab. I wanted to plot pdf of random variable y which is funtion of x. f(y)=aX^3+b. X is Gaussian random variable with zero mean and unit variance. By simplification pdf of y was obtained as:
> pY(y)=1/(3a*[〖(y-b)/a〗^(2/3)]*√2pi) e^(-1/2 [(y-b)/a〗^(2/3)])
> that is in usual case we plot pdf of a variable x. here x=(y-b)/a
> This is a problem found in Proakis Digital communication textbook. #2.4

What is your question related to MATLAB?

"Jyothy MJ" <jyothymj@gmail.com> wrote in message <i7j2op$3q$1@fred.mathworks.com>...
> Hi,
> I'm a beginner in Matlab. I wanted to plot pdf of random variable y which is funtion of x. f(y)=aX^3+b. X is Gaussian random variable with zero mean and unit variance. By simplification pdf of y was obtained as:
> pY(y)=1/(3a*[〖(y-b)/a〗^(2/3)]*√2pi) e^(-1/2 [(y-b)/a〗^(2/3)])
> that is in usual case we plot pdf of a variable x. here x=(y-b)/a
> This is a problem found in Proakis Digital communication textbook. #2.4
- - - - - - - - - - -
  I think you are asking us how to derive the pdf of your defined y random variable. Here's a hint: Remember that the probability density of random variable y at a point can be defined as the derivative with respect to y of the cdf of that random variable there and therefore if you are deriving it from the cdf of a different variable x, it will necessarily have to involve dy/dx at some point. Does that help? Was that what you wanted? You didn't really ask a question.

Roger Stafford