ASSIGNMENT( BAYES THEOREM)1. A manufacturing firm produces steel pipes in three plants with daily production volume of 500, 1000 and 2000 units respectively. According to past experience it is known that the fraction of defective output produced by the three plants are respectively 0.005, 0.008 and 0.010. If a pipe is selected from a days total production and found to be defective.(i) Find out from which plant the pipe came.(ii) What is the probability that it came from the first plant?2. A company has two plants to manufacture scooters. Plant I manufactures 80% of the scooters and plant II manufactures 20%. At plant I, 85 out of 100 scooters are rated standard quality or better. At plant II only 65 out of 100 scooters are rated standard quality or better.(a) What is the probability that the scooter selected at random came from plant I if it is known that the scooter is of standard quality?(b) What is the probability that the scooter selected at random came from plant II if it is known that the scooter is of standard quality?3. Each of the three the same jewellery boxes has 2 drawers. In each drawer of the first box there is a gold watch. In each drawer of the second box there is a silver watch. In one drawer of the third box there is a gold watch while in the other drawer there is a silver watch. If we select a box at random, open one of the drawers and find it to contain a silver watch , what is the probability that the other drawer has the gold watch?

ASSIGNMENT (RANDOM VARIABLE)1. The probability that there is at least one error in an account statement prepared by A is 0.2 and for B and C they are 0.25 and 0.4 respectively. Find the expected number of correct statements in all.2. If four unbiased coins are tossed, find the expectation and variance of the number of heads.3. A man has the choice of running either a hot- snack stall or an ice-cream stall at a sea side resort during the summer season. If it is a fairly cool summer he should make Rs. 5000 by running the hot snack stall, but if the summer is quite hot he can only expect to make Rs. 1000. On the other hand if he operates the ice-cream stall, his profit is estimated at Rs. 6,500, if the summer is hot, but only Rs. 1000 if it is cool. There is a 40 per cent chance of the summer being hot. Should he opt for running the hot-snack stall or the ice-cream stall? Give mathematical arguments?4. A firm plans to bid Rs. 300 per tonne for a contract to supply 1,000 tonnes of a metal. It has two competitors A and B and it assumes that the probability that A will bid less than Rs. 300 per tonne is 0.3 and that B will bid less than Rs. 300 per tonne is 0.7. If the lowest bidder gets all the business and the firms bid independently, what is the expected value of the contract to the firm?5. The monthly demand for transistors is known to have the following probability distribution:

Demand(X): 123456Prob(P) : 0.10 0.15 0.20 0.25 0.18 0.12

Determine the expected demand for transistors. Also obtain the variance. Suppose that the cost (C0 of producing x transistors is given by the rule , C= 10,000 + 500*x. Determine the expected cost.