I would not trust the jre from the install. Not to mention that is were the install stops
I usually just install the sdk cause i use to work in a dev enviroment.
over to the right is popular downloads click J2EE1.4SDK in the Separate Bundles section click J2SE 1.4.2 DOWNLOAD except the agreement. Then download....
Linux version of course "self-extracting file (j2sdk-1_4_2_04-linux-i586.bin, 34.17 MB)"
save it to your home dir.
By convention I install things in /usr/local and I usually give my user ownership over that dir, but you can put it were ever you want just change things acordingly.
mv j2sdk-1_4_2_04-linux-i586.bin /usr/local/
chmod 777 j2sdk-1_4_2_04-linux-i586.bin
agree with terms
rm -rf j2sdk-1_4_2_04-linux-i586.bin
ln -s j2sdk1.4.2_04/ java
JAVA_HOME=/usr/local/java export JAVA_HOME
and add to your path
PATH=$JAVA_HOME/bin export PATH
Make sure you invoke your profile
then you should be able to echo $JAVA_HOME