ANSWER THE FOLLOWING.

IMAGE 1 IS QUESTION 1,

IMAGE 2 IS QUESTION 2 ,

IMAGE 3 IS QUESTION 3

b) The discrete random variable X has the probability function k(x2 9) x = 4,5,6 0 otherwise Where k is a constant i. Show that k = % =(3 marks) ii. Find E (X) and Var(X). (6 mark) 1 Ex, 05x52 A continuous random variable X has a pdf given by f (x) = 0 nd the mean and standard elsewhere ' of X Amarks) Each child born to a particular set of parents has probability 0.25 of having blood type 0. If these parents have 5 children i. What is the probability that exactly 2 of them have type 0 blood? (2marks) ii. What is the expected number of children with type 0 blood? (Zmarks) a) The following 11 = 10 observation are a sample from a normal population mmm-l! i. Find the mean and standard deviation of this sample (4marks) ii. Find a 99% condence interval for the population mean u (4marks) b) The length of human pregnancies from conception to birth approximates a normal distribution with a mean of 266 days and a standard deviation of 16 days. What proportion of all pregnancies will last between 240 and 270 days (roughly between 8 and 9 months)? (3marks) c) X is a continuously and uniformly distributed on the interval (0,50). Find the Expected Value (E [x]) and Variance (Var(x)) of X (4marks) a} A student has collected the following data describing the prices and quantities of harvested crops for the years 1990, 2000 and 2004 (Price in lggh, and Production in kgs). _ Price Production Price [m "m _ Wheat 1220 1450 800 m 1000 Construct the Fisher's price Index in 2000 and 2004, using 1990 as the base period. Give your comments on the results. (Gmarks)