You are watching two items posted for sale on eBay and bid $30 for the first and $20 for the second item. You estimate that you are going to win the first bid with probability 0.1 and the second bid with probability 0.2, and you assume that winning the two bids are independent. Let random variable Y denote the total number of winnings for these two bids. Let random variable X denote the total amount of money you will spend on the two items.

(a) List the sample space of all possible outcomes of winning or losing the two bids. (Use W for winning L for losing. For instance, WL represents 'winning the first bid but losing the second bid'). Find the probability of each outcome in the sample space.

(b) Find the probability distribution of Y , the total number of winnings for these two bids. Does Y follow a binomial distribution? Explain why.

(c) Find the probability distribution of X, the total amount of money you will spend on the two items. (Note: if you lose both bids, you will spend $0.)

(d) Find and interpret the expected value of X.

(e) Find the variance and standard deviation of X.