Recall the hat problem: n people show up at a party and throw their hats into a basket. The hats are shuffled. Each person picks a hat at random from the basket. Let X be teh random variable describing the number of people who get back their own hats. You already showed in a previous homework assignment that E[X] = 1 for all n. Now Show that V[X] = 1, for all n. Hint: Use the formula, proved above: Ex. = [VIxil+ [ Cor(X, X;). ifj n people show up at a party and throw their hats into a basket. The hats are shuffled. Each person picks a hat at random from the basket. How many people get back their own hat