3. You must use properties of linear combinations of random variables to solve these problems. (a) Let X be a random variable where ux = 3, 0x = 9. Find the mean and the variance of Y, where Y = -2+4X (b) Let X be a random variable where (x = 0, of 1/4. Find the mean and the variance of Y, where Y = -10- 3X 4. Answer the questions with TRUE or FALSE and explain your answers as well. (a) If we have 5 binomial trials, and Y =# of successes in the 5 trials, Y can take on only values {1, 2, 3, 4,5}. (b) If a random variable Y only takes on values {0, 0.1, 0.2, 0.3, 0.4}, it is a discrete random variable. (c) The probability of the intersection of two events could be higher than the probability of the union of two events.1. The number of moles on a persons face can be consid ered a discrete random variable, and assume it has the following distribution: Number Moles (Y) 0 1 2 3 Relative Freq 0.72 0.16 0.09 0.03 (a) What is the probability that someone has more than 1 mole? (b) What is the probability that someone has between 0 and 2 moles (inclusive)? (c) Find the expected number of moles someone has. (d) Find the variance of the number of moles someone has. 2. Hospital records show that for patients suffering from a certain disease, 15% die from it (regardless of the pa- tient). Assume patients are independent, and that 8 pa- tients are observed. (a) What is the probability that exactly 4 patients re- cover? (b) What is the probability that between 1 and 3 patients die (inclusive)? (c) What is the expected number of patients who die out of the 8? (d) What is the the standard deviation of the number of patients who die out of the 8? (e) What is the probability that at least 3 patients die