1. The table shows the probability distribution of a discrete random variable X, where k is a constant. (3) Find it. (3 marks) (b) Find EBOOX +13)_ (0 If 13(30th +13) :Var(mX - 20) (3 marks) where m is a positive constant, find to. (4 marks) 2. The number of cars passing through a road in 1 minute follows a Poisson Distribution with mean 5. (a) Find the probability that there are 2 cars passing through the road in one minute. (3 marks) (I1): Find the probability that there are 4 cars passing through the road in two minutes. (3 marks) (1:) Find the probability that there are 4 cars passing through the road in two minutes given that there are 2 cars passing through the road in the first minute. (4 marks) 3. Suppose that the heights of college basketball players are normally distributed with a mean of '74 inches and a standard deviation of 4 inches. (a) What percentage of players are over 84 inches? (2 marks) (b) What is the value of the 95* percentile? (2 marks) Ten college basketball players are randomly selected to measure their height. (c) What is the probability the mean height in the sample is over 72 inches? (3 marks) (d) If 99.49% of the sample means are taller than a specific height Y, find Y. (3 marks) (On doing Q3, please refer to your normal distribution table in your notes)