Your three friends Gigi, Harry and June are having a joint birthday party this year. Unfortunately, you procrastinated on buying them birthday gifts! Now it's getting late and the only option is buying them gift cards from Dunkin'. The gift cards come in value $10, $20, and $50. Since you love playing cards, you decide on the following randomized strategy for how much to spend. For each of your three friends independently, you will shuffle a standard deck of 52 cards and pick a card at random. If it's a 2 through 10, you will spend $10; if it's a Jack, Queen or King, you will spend $20; and if it's an Ace, you will spend $50.

(a) Identify the sample space of this experiment. Then define a random variable X associated with the total amount you spend on all three friends.

(b) Compute the PDF of X.

(c) Compute the CDF of X.

(d) What is the probability that you spend more than $75 in total?