Need to solve the problem and explain as much as can.

I. If the values ofthejoint probability of X and Y are as shown in the table. (GM your answers as fractions) I 0 l 1 1 12 6 y 1 1 4 4 1 1 3 20 3 1 120 Find. a} \"1-1) h) F(1,1) C) f(2|1) d) an 2. It is known that in a certain industry 60 percent of all labour-management disputes are over wages, 15 percent are over working conditions, and 25 percent are over fringe issues. Also, 45 percent of the disputes over wages are resolved without strikes, 70 percent of the disputes over working conditions are resolved without strikes, and 40 percent of the disputes over fringe issues are resolved without strikes. (Give your answer up to 3 decimal places) a} What is the probability that a labour management dispute in this industry will be resolved without a strike? b) What is the probability that if a labour-management dispute in this industry is resolved without a strike, it was over wages? 3. There are 90 applications for a job at a television station. Some of them are college graduates and some are not; some of them have at least three years of experience and some do not, with the exact breakdown being College graduates Not college :4 duates At least 3 yeats of experience Less than 3 years of experience The applicants are interviewed in random order. G is the event that the applicant interviewed is a college graduate, and T is the event that the applicant interviewed has at least 3 years of experience. Calculate the following: (Givewur answers up to 2 decimal places) a) PU?) b) P(T|G) c} PIZG' IT') {1) P05 ' n T') 4. Explain (in one sentence) why there must be a mistake in each of the following statements. (a) The probability that Jean will pass the Joint Entrance Examination is 0.66 and the probability that she will not pass is - 0.34. (b) The probabilities that a secretary will make 0,1,2,3,4 or 5 or more mistakes in typing a report are, respectively, 0.12, 0.25, 0.36, 0.14, 0.09, and 0.07. 5. If the random variables X, Y and Z have the means (x = 2, My = -3, Uz = 4, variances of = 1, 0% = 5, 0? = 2 and covariances oxy = -2, 0yz = 1, 0xz = -1. Find the mean and variance of W = 3X - Y + 2Z