Please put down all steps and details D) Find the expected value of a die roll. Do not round. E) Find the variance of a die roll. Do not round. F) Find the standard deviation of a die roll. Round to two decimal places.

Question 1 Suppose an unfair die is rolled. Let random variable X indicate the number that the die lands on when rolled and assume the probability distribution below. X 1 2 3 4 5 6 Pr( X= x ) 0.05 0.10 0.20 0.27 0.15 0.23 A) Find the probability of rolling a 2 or 3. B) Find the probability of rolling a number that is at least 4. C) Find the probability of rolling a number less than 3