Answer multiple choice q

Exercise 1.1 (5pts) Let X be a random variable with possible values 1, 2, 3, 4, and corresponding probabilities P( X = 1) = p. P(X = 2) = 0.4, P(X - 3) = 0.25, and P(X = 4) = 0.3. Then the mean of X is: a. cannot be determined b. 2.75 + p c. 2.8 d. 2.75 Exercise 1.2 (5pts) The estimated regression line: a. does not change the sum of squared residuals. b. maximizes the sum of squared residuals. c. minimizes the sum of squared residuals. d. sometimes maximizes and sometimes minimizes the sum of squared residuals. Exercise 1.3 (5pts) If an estimated regression line has a slope of 16, an intercept of 4, and the mean of the input variable is 8, then the mean of the response variable is: a. 64 b. 8 c. 132 d. 48 Exercise 1.4 (5pts) A farmer recorded the weights of 25 randomly selected pigs from his farm. A 95% confidence interval for the mean weight was calculated to be from 280.2 to 289.8 pounds. What is being estimated by this confidence interval? Choose one: a. the weights of all pigs at this farm b. the mean weight of 25 pigs at this farm c. the mean weight of all pigs at this farm. d. the middle 95% of weights for pigs at this farm