Two questions:

Consider the following grading system: Based on the previous years, we know that the professor grades an exam work as "very gnod'1 with a probability of {12; as 1"good" with a probabilit},r of 0.35; and as "satisfactory\" with a probability of 0.25. Consider a random variable A describing the distribution of grades in the exam. What are the probabilities of pasting; an exam with other grades {according to the table] if we know that the expected value of a random 1variable A is equal to 2.5? Consider the following dice game where the player bets one euro and chooses a number between 1 and 6, e.g., 2. Then the player rolls a die three times and receives: . nothing, if no 2 are thrown; . 2 euro, if 2 is thrown once; . 3 euro, if 2 is thrown twice; . 4 euro, if 2 is thrown three times. The outcome is the same for all other possible numbers the player can choose (e.g., if the player picks 5, then after rolling a die three times, the number of fives will be counted). Define a random variable Z that describes the player's profit after one round of the game (do not forget that, to start the game, the player pays 1 euro). Calculate the probabilities P(Z = -1). P(Z = 0), P(Z = 1), P(Z = 2), P(Z = 3), as well as the expected value, the variance, and the standard deviation of Z