A student receives pocket money from his family as follows: Some amount (let's denote by x) is written on a yellow paper. Then, a coin with a probability of 0.3 to hit the head is tossed and the result is not told to the student. On a red paper, if the result comes to a head, 3x is written x / 4 (for example: 10 T on yellow paper; 30 on red paper; 2.5 on red paper; T is written). Both papers are brought in front of the student and asked to make a choice. After the student opens the paper he has chosen, he can accept the amount written or replace it with the other paper (he does not know the amount written on the other paper). the student aims to receive maximum pocket money. Accordingly,
a) In terms of expected earnings, which card is it reasonable to choose? Is it necessary for the student to replace the selected paper with another paper after seeing it?
b) the student is thinking of a strategy: the student determines a quantity in his head, denoted by y. He then opens the red paper. It accepts if the amount written is not less than y. If the amount on the red paper is greater than y, it deforms it with yellow paper. E [H (x, y)] =?