3. Among 150 students enrolled in Introductory Econometrics, 30% of them spent 4 hours, 50% spent...

 

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3. Among 150 students enrolled in Introductory Econometrics, 30% of them spent 4 hours, 50% spent 6 hours, and 20% spent 8 hours a week for their study. (a) Let X represent study hours per week. Explain why X is considered as a random variable. (b) Find the expected value of X and the variance of X. [2 marks] (d) Find the expected value of the sample mean. What is your observation? [3 marks] (c) Random samples of two students are drawn with replacement. Find the probability distribution for the 5 possible values the sample mean can take. [3 marks] [2 marks] 3. Among 150 students enrolled in Introductory Econometrics, 30% of them spent 4 hours, 50% spent 6 hours, and 20% spent 8 hours a week for their study. (a) Let X represent study hours per week. Explain why X is considered as a random variable. (b) Find the expected value of X and the variance of X. [2 marks] (d) Find the expected value of the sample mean. What is your observation? [3 marks] (c) Random samples of two students are drawn with replacement. Find the probability distribution for the 5 possible values the sample mean can take. [3 marks] [2 marks]