Problem #3: (20pts) The probability distribution for the random variable X is given by x 2 3.5 4 4.5 5 P(X = x) 0.1 0.2 0.3 a 0.15 a) What is the value of a? b) The variable x is sampled 10,000 times. How many times would you expect x to have a value between 3.5 and 4.6, inclusive? c) Calculate the mean and the standard deviation of x. d) Calculate the mean and the standard deviation of the random variable x+4.