Final Exam - Summer 2020 1. A) Define conditional probability. B) If P(A) = 0.53, P(B) = 0.61, and P(A  B) = 0.85. Compute P(A | B) and P(A' | B') 2. A. State Bayes’ Theorem B. There are three...

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Final Exam - Summer 2020 1. A) Define conditional probability. B) If P(A) = 0.53, P(B) = 0.61, and P(A  B) = 0.85. Compute P(A | B) and P(A' | B') 2. A. State Bayes’ Theorem B. There are three groups. The first group consists of 20 girls and 25 boys. The second group consists of 25 girls and 20 boys. The third group consists of 23 girls and 22 boys. one of the three groups was chosen randomly, and, a person was chosen from it and found out to be a girl. Find the probability the girl was from the second group. 3. Compute E(x) and (x) if x follows the following probability distribution x 5 1 2 3 4 p(x) 0.1 0.2 0.1 0.2 4. Find the coefficient of variation of the data: 20, 27, 25, 33, 31 5. Compute Cov(x, y) and co-relation coefficient if (x, y) follows a joint distribution P(x, y) given below: 6. A random sample of 100 households had an average annual income of $78,350 per year with the standard deviation $2,520 per year. Find the confidence interval of the average household income at a 95% level. 7. A random sample of households had an average annual income of $78,350 per year with the standard deviation $2,520 per year. Calculate the minimum sample size needed to identify a confidence interval of the average annual income of families within an error of $3000 at a 99% level. Final Exam - Summer 2020 8. Out of a random sample of 400 people selected from a large group, 183 people speak at least two languages. Find the confidence interval of the proportion of the people who speak at least two languages at the 90% level. 9. The following is the data of the amount of garbage produced by households in a neighbourhoods in Kg. 3.0 6.5 6.0 5.5 20.5 7.5 12.0 20.5 11.5 17.5 A) Find the confidence interval of the average amount of garbage produced by the householdsat a 90% level. B) Find the confidence interval of the variance of the amount of garbage produced by the households at a 99% level. 10. A computer company claims that its laptop batteries average more than 3 hours of use per charge. A sample of 25 batteries last an average of 3.05 hours. Assume that the population standard deviation is 0.7 hours. Test the claim at  = 0.05.