I have questions about random variables. I tried to solve them, but I got the wrong answer for 72, which is 5/36. Also, about #68, I am not sure how I make an equation for ", I will pay you 15 unless it is an ace in which case you will pay me 100." Could you give me some tips?

Thank you

The correct answers:

68(a). -1/13 (b). 850.686, 72. 104/225

68. You have a standard deck of playing cards. There are 52 cards. There are 4 suits. Each suit has cards numbered from 2 to 10 and then four face cards (jack, queen, king and ace). You randomly draw a card from the deck. I will pay you the number on the card. If you draw a face card, I will pay you 15 unless it is an ace in which case you will pay me 100. Let X be the random variable representing the amount of the payment. a. Calculate the E[X] from your standpoint. b. Calculate the Var[X] . \f