Q 1. (a) If X is the random variable model 'the number on a biased die', and the probability distribution function of X is as shown below, X 1 2 3 1/6 1/5 4 5 6 P(X=x) K 1/5 1/6 (i) For a computed value of k, critically analyze and comment on the Standard deviation of X. AP [4] (11) Given an expected function of E(5x2 - 6x + 7),explain this function as against Probability distribution function of X as shown above. AN [3] (b) Construct the Probability distribution function of T for a given random variable defined as 1/72 (2t - 1); T = 1,2,3,4,5,6 , and comment analytically on the variability of the given computed var(X). AN [3] (c) Consider the following function for a value of C. 2/7 CX f(x) = 2c(3-x) , , Oxs2 25x54 0 , otherwise Comment on the output of these probabilities below, what will be the conclusion of your output. (i)Evaluate c. EV [4] (ii) find (a) P(1 = x s 2) CR [3] (B) P(x > 2). CR [3]