Question

If there are 6 bags and each of them containing 6 balls.

Suppose x th bag is containing x red balls and 6-x blue balls.

A fair die is roIled to obtain a number x in {1,2,...6}, and so I pick a ball from x th bag.

Let Y=1 if a red ball is picked from x th bag andY=0 if blue ball is picked.

1, E[y|x] and E[y]

2, var[y|x] and var[y]

Answer 1

1.

since there are total 6 balls in the xth bag and out of them x are red balls and 6-x are blue balls.

Now ,

   Here x can be one of with probability

So,

2.