(Answered)-I have four different sweaters. Every day I choose one of the - (2025 Updated Original AI-Free Solution

Question

1. I have four different sweaters. Every day I choose one of the four sweaters at random to wear. Let X be the number of different sweaters I wore during a 5-day week. (For example, if my 5-day sweater sequence is (3, 2, 4, 4, 2) then X = 3 because that week I wore sweaters 2, 3 and 4.) Find the mean and variance of X.