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a. Given the population covariance, γ, is defined as E[(X−μX)(Y−μY)], show that this can also be expressed as E[XY]−E[X]E[Y]. (3 marks) b. A sample correlation coefficient of r=−0.6241 was found for 15 paired observations. Using α=0.05, test if this value is significantly different from zero. (3 marks) c. The examination marks of thirteen students in two statistics papers (a foundation paper, Pape I, and a more advanced paper, Paper II) were as follows: The summary statistics for these data are: ∑xi=856∑yi=1041∑xi2=58402∑yi2=84801∑xiyi=70203 i. Calculate the sample correlation coefficient and comment. ii. Determine the line of best fit of y on x. iii. If you were told a student achieved a mark of 68 in Paper I, compute a 95\% prediction interval for the students mark in Paper II. (14 marks)