We have an infinite sequence of independent variables where we take k labelled balls and put them into k labelled slots so that there is one ball per slot. We want to find the expected value and variance of Xn (the number of balls that have been placed in a slot matching their number). So, X1, X2,.... is an infinite sequence.
I am mainly struggling with how to approach the question. Why is it infinite if we only have k balls?
Should I start with indicator functions?