PL/SQL :: Input Parameter Of Table Type And Null Assigned To It

I have few questions regarding PL/SQL tables

1) If I don't specify the "INDEX BY" clause, it is indexed by PLS_INTEGER by default, right?

2) Consider this package specification

CREATE OR REPLACE PACKAGE Testxyz AS
TYPE tab_Numbers IS TABLE OF PLS_INTEGER;
PROCEDURE TestNumber(ptab_Numbers IN tab_Numbers := NULL);


END Testxyz;So I created a table (I hope it is defaultly indexed by pls_integer data type) and I am passing it as a parameter to a procedure. Because I want this parameter to be optional I am assigning null into it.

Now I change the definition of the table to:

CREATE OR REPLACE PACKAGE Testxyz AS
TYPE tab_Numbers IS TABLE OF PLS_INTEGER INDEX BY PLS_INTEGER;
PROCEDURE TestNumber(ptab_Numbers IN tab_Numbers := NULL);
[code]....

3) Because I need this parameter to be optional, I use the first declaration:

CREATE OR REPLACE PACKAGE Testxyz AS
TYPE tab_Numbers IS TABLE OF PLS_INTEGER;
PROCEDURE TestNumber(ptab_Numbers IN tab_Numbers := NULL);
END Testxyz;

Now I create an anonymous block and want to assign something into the table

DECLARE
   vtab_Numbers TESTXYZ.tab_Numbers;
BEGIN
vtab_Numbers(1) := 5;
END;
/When trying to run this, I got:
06531. 00000 - "Reference to uninitialized collection"

Is it possible to have input parameter of PL/SQL table type and have defaultly null assigned to it?