Q-1: Probabilistic Models (CLO 2) (10 Marks) a) Solve the following 1. For the function p(x) given by Figure 1 below, calculate the Cumulative Distribution Function for all samples greater than 1 and less than or equal to 4. Figure 1 2. If a data array is being passed to a clustering algorithm, but a pre-processing phase has been added to assign weights to the strings, keeping that in view solve the following problem: Assume the string S = {T', 'stay, do', 'not, 'safe', 'home', 'flu'} where the words in D have the probability distributions as: [0.5, 0.5, 0.3, 0.02, 0.02, 0.02 0.04 ) If a random pattern generated is 'Istayhome' having a cumulative probability of 0.005, then what would the most optimal combination of occurrence of five consecutive words. Calculate the combination and draw a flowchart of your pre-processing algorithm. 3. If you are a participant in "Jeeto Pakistan' and you are down to three Boxes in value Rs. 1, Rs, 2.5 Lakh, and Rs. 10 Lakh you are offered a deal of Rs. 4 Lakh, would you take the deal? (Show Calculations) 4. If a disease is fairly rare and the antibody test is fairly expensive, in a resource-poor region, one strategy is to take half of the serum from each sample and pool it with n other halved samples and test the pooled lot. If the pooled lot is negative, this saves n-1 tests. If it's positive, then you go back and test each sample individually, requiring n+1 tests total. 1 a) Suppose a particular disease has a prevalence of 15% in a third-world population and you have 500 blood samples to screen. If you pool 20 samples at a time (25 lots), how many tests do you expect to have to run (assuming the test is perfect)? and What if you pool only 10 samples at a time