Question

1. A bag contains 4 red and 5 green balls. Let X denotes number of red and Y denotes number of green balls in 2 drawn from the bag by random. Find joint probability distribution, compute E(x), E(Y) and correlation coefficient. 2. A diagnostic test has a probability 0.95 of giving a positive result when applied to a person suffering from a certain disease, and a probability0.10 of giving a (false) positive when applied to a non-sufferer. It is estimated that 0.5 % of the population are sufferers. Suppose that the test is now administered to a person about whom we have no relevant information relating to the disease (apart from the fact that he/she comes from this population). Calculate the following probabilities: (a) That the test result will be positive; (b) that, given a positive result, the person is a sufferer; (c) that, given a negative result, the person is a non-sufferer; (d) That the person will be misclassified.

Answer 1

solution: shop: x donoted ~ Rod balls y doooles balls gxoon Ime random draw a balls flere. probability we remember joint P(x, y) yor 2920 Sol Play) + pouchability distribution to red balls is doocan; X 0 2 pla) 5118 519 16 balls dequins & poroba porobability dos teribution of glisens 0 ㅗ 2 ply) 16 519 | 5/18 stepa 0 The joint probability is ly 0 닌 2 o 5/18 5191 4 o 0 o o

5 step3: calculate Courelytion coefficient, cov (814) lay ory E(x) = f(x) ECM) - ((V)? Gay stept! Here €(4) - Cover )+(+YS/a) + (227) 819 ECHT = (3/9) 64- 81 puso pX5 + l/a - Elxy )+(x512) +(27x96) 0+519+416 (0x76) + 1x574) +(2 89718) slepsi Ely) Z z flyg Halla 11a 121/82 (aha pero (6x76) + (1x5%) +(8x578) SLS E14,4) stepe -519 EXY) - EC99%= - Go -14 E(YY) – E(YN 5- 121 G4 - 35 81 81 ho 3 81

stept. Correlation coefficient s cov (%94) Y GY (-43131) z 35 14 :) 81 z - 7. 1332