Probability and Statistics

Can you please answer these 2 questions below 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 variance of X? * O -3/3 9/2 371/64 35/4 75/2 OOOOO 635/16 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 * O E[Y]=1, Var[Y]=1 O E[Y]=3/2, Var[Y]=15 E[Y]=2, Var[Y]=1 E[Y]=3, Var[Y]=7/8 E[Y]=7/2,Var[Y]=1 O O E[Y]=5/2, Var[Y]=35/16 O O \f