1. The probability distribution for random variable X is given in Table 1. x o 1 2 P(X=x) l E l 4 4 4 Table 1: Probability distribution for X (a) Compute the following : i. Mean and variance ii. Standard deviation iii. E(2X + 24) (5 marks) (2 marks) (3 marks) For the continuous random variable X, the probability distribution is given by f(x)={ 0((x2+1) 15xs_4- 0 0therw15e (a) Find i. The value of the constant a. (4 marks) ii. E(X). (4 marks) iii. Var(X) (4 marks) iv. P(1 s X s 3) (4 marks) (b) M is discrete random variable that has the expected value 25 and variance 3. Find: i. E(3M +24) (2 k ) mar 5 ii. Var (2M 14) + E(4M) (2 marks) 3. There is a bag filled with 2 blue, 8 red and 2 yellow. Aireen picks a marble out the bag, notes its colour and replaces it. She then takes another marble from a bag. (a) Draw a tree diagram to represent the experiment and state the sample space S for the experiment. (6 marks) (b) What is the probability of: i. getting 2 reds? (2 marks) ii. getting 2 blues? (2 marks) iii. getting 2 yellows? (2 marks) iv. getting 2 different colours? (3 marks) (c) A number from 1 to 20 is chosen at random. What is the probability of choosing; i. an even number? (2 marks) ii. prime number