I need help with this problem If anyone can be so kind in helping me do the questions for me? thanks!

3. You paid $15!] for the box of illtl lighthulhe in the previous question so the cost oleachbulb is $1.511 But in order to keel: you as a happy mstDmJe; for each defeative bulbyou take back I—ISU will refund refund $1l] for your trouble. For example, if you findtwo defeative bulbs ttmy will refund $20 eoefl‘ecfively you have only paid $15!} — 35213 = $13!] for the box. Let Y be the effective cost of a box ofbulhe. Noting that the effieaflvecoetis $13D only wtten there are two defeafive bulbe which inturn happens 20% ofthetime we see that Pg}? =13CIJ= [ill]. {E} Find the Sample Space modeled with the random variable 1". (b) Give a table diaplaying the probability mass function of 1". {c} Find the expected Value, varianee, and standard deviation of Y.