Can I distribute a JDK with my application?

I am working on an application called Enchanting. The application, based on Scratch, emits Java source code and compiles it for uploading onto LEGO Mindstorms NXT Robots.

While the application is very early, users have a hard time installing it.

Right now Windows users have to:

• download and install a Java Developer Kit
• download and install LeJOS (a java library for the NXT)
• possibly tweak environment variables
• then they can download, install, and run Enchanting itself

If I could provide an installer that would include the JDK, and LeJOS, I could figure out the environment variables at run time, and the process becomes:

• Download, install, and run Enchanting

Is there a way to redistribute a JDK?

(Incidentally, Processing (a simplified text-based programming environment) seems to offer a version that comes with the JDK, so it appears that there is a legitimate way to do so).

Addendum: I would like a Windows user who does not have java installed to be able to run a single .exe file to install the JDK, LeJOS, and Enchanting.

The information regarding redistribution is here for Java 10 JDK and here for Java 8 JDK. Currently Java 8's is substantially more detailed than Java 10's.

and you can use PackJacket, to package all the files you need and create an installer.