Probability and Statistics

Can you please answer the questions and show your work. thank you

• A game played with a fair eight-sided die, as pictured below. The player rolls the die. The player loses $6 if a 1,2,3, or 4 is rolled. On a roll of 5, 6, 7, 8 the player wins that amount.

Let X be the random variable representing the players wins/losses in dollars. What is the expected value of X? * Let X be the random variable representing the players wins/losses in dollars. What is the variance of X? * Suppose the game is played 20 times. Let Y be the random variable that counts the number of times that an 8 is rolled. The expected value and variance of Y are * \f