When you do laundry sometimes you lose 1 or 2 socks. The probability you lose 1 sock is .80 while the probability you lose 2 socks is .05. Assume that you cannot lose more than 2 socks. a) Find the expected value and the standard deviation of the number of socks you lose when you do laundry once.

b) Find the standard deviation of the total number of socks you lose when you do laundry three times. You can assume that the numbers of socks you lose in different washes are independent. You can assume that the probabilities of losing 0,1 or 2 socks don't change between different washes.