CDF-vector- 2 random variables

I have an equation with 2 variables, x and y. x and y are random variables. The question is: Ln(Z)=aLn(x)+bLn(y)+c a,b and c are constant and already determined. I need to calculate CDF of Ln(Z). I need to obtain a surface (3D) by Matlab. I will appreciate your help.

Thanks

[Jeff Miller]

What are the distributions of the random variables x & y, e.g., normal, uniform, gamma? Or are x & y vectors of observed data values and you don't know their theoretical distributions?

Are x & y independent?

[Ahmad DEHGHANPOOR]

Hi Jeff, Thanks for your reply, x and y are independent. They have alreday determined:

x= 15:15:150

y=0.5:0.5:5

x and y are based the above data.

the actual equation is :

Ln(Z)=1.302Ln(x)+0.2Ln(y)-0.12

I have attached a similar graph that I need to obtain.

Answer 1

[Jeff Miller]

You apparently have a probability for each of the x and y values. So, you can just compute the different possible Ln(Z) values from your equation. With independence, the probability of each Ln(Z) is the product of the probabilities for the x and y used to compute it.