BigQuery average on parent and child

I’m trying to get average count of child items.
I have a table like below

parent_id| child_id | Type 
1        | 11         | A
1        | 11         | B
1        | 12         | A
1        | 12         | B
1        | 13         | A
2        | 14         | A
2        | 15         | B
2        | 15         | A

In the output I want to know for a given parent_id, what is the average count of A and average count of B.
I achieved that using groupby.
But wanted to check if in the same query I can get the average count of A for child_id also?
In short getting average count of Type per child and add a column which will tell me average count of Type per parent_id also.

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