How to rewire outside camera?

[Unused Classified <strangways@xxxxxxxxx>]

Hello,

I had a DVR security system installed in my house 2 years ago.

One cam is up a tree in the back yard and it stopped working.

I climbed up the tree to check the connection, the power connection is
okay but the video connection is rusted and ruined and I had to cut it
out.

Now I have two wires that need connectors and then need to be spliced
together.

The cable that runs from the house is like a thick cable TV cable.

The other one, the one from the camera,  is much thinner, and the
connector was like a stereo plug.

What=92s the best way to splice these wires considering they have to
survive the rain and cold?

I know I could buy the 2 connectors, splice the wires and wrap them in
tape and the plug them into an adapter.

This would be more vulnerable than the connection that just rusted.

Is there a better way? Thanks