High School How to combine 2 distributions with different sample sizes?

[batmantrippin]

TL;DR

I would like to know how to combine 2 distributions with different sample sizes and have a new 3rd distribution.

I apologise in advance for what is a very basic question for someone with a maths degree (it was a long time ago!).

I have 2 distributions that look something like this (but with much bigger samples), in the form of (probability,outcome). The outcome is literally just a number.

Distribution 1:
(0.1 , -1)
(0.2 , -0.9)
(0.25 , 0)
(0.3 , 4.5)
(0.15 , 7)

Distribution 2:

(0.05 , -1)
(0.05 , -0.8)
(0.05 , -0.5)
(0.05 , -0.2)
(0.1 , 0)
(0.1 , 3)
(0.1 , 6)
(0.1 , 6.5)
(0.2 , 7)
(0.2 , 7.5)

What is the best way to combine (average?) the two and have a third distribution in the same format that is basically an average of the two? Or am I asking for something that's not really doable?

 

[mathman]

Add them with weights proportional to the sample sizes.

 

[Dale]

The procedure described by @mathman gives what is called a mixture distribution.