When we analyze data , we can observe several variables that may contain mutual information. For an example , There can be a binary variable such as Y=Have you ever smoke ? And then there will be a follow up question such that (in this case it is a continuous variable) How old when you first smoke ? 

For the variable X=that measures How old when you first smoke ? ,

$X\_1$= {$x\_1$=0 ; if never smoke,
 $x\_1$=1 ; if smoke
}

$X\_2$ = {$x\_2$=0 ; if $x\_1$=0
 $x\_2$ >=0 ; if $x\_1$=1
} 

So the distribution of $X\_2$ will be like this :

[![enter image description here](https://i.stack.imgur.com/TS5To.png)](https://i.stack.imgur.com/TS5To.png)

That means it contain several zeros since it is depends on the previous question ($X\_1$)

One way to deal with this type of problem is calculate the age of first smoke ($X\_2$) only for users. (i.e eliminating zeros) . Then the drawback is that it will reduce the sample size with respect to $X\_2$ variable. 

Another way to model $X\_2$ is convert it to a categorical variable. For an example someone can do like this: 

$X\_2 categorized$ ={"Never Smoke" ; $X\_2$=0 , "Young" ; 0< $X\_2$ <=15 , "Middle" ; 15< $X\_2$ <=20 , "old" ; $X\_2$>20} 

But Is there way to Model X by preserving the continuous nature using a mixture distribution ? Mixture distribution in the sense that ,this may be something like the product of $X\_2$ and $X\_1$. However I am not sure how to do this .

Since in this case $X\_1$ is binary , taking the product of $X\_2$ and $X\_1$ seems to make sense. 
But I am not sure how this will work in general , i.e when $X\_1$ has more than 2 categories.

Any help would be great