Simulation study plays an important role in statistics and data science. It provides a fundamental tool...

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Simulation study plays an important role in statistics and data science. It provides a fundamental tool to study the properties of statistical estimators and models under various situations, because in simulation study, we know the "ground truth" of the data, which we seldom have in real-world data analysis. In this question, we are going to perform a basic simulation study related to the standard normal distribution. a. [2 points] Compute the proportion of values smaller than 1 for a standard normal distribution. b. [7 points] Write a function called stats_normal with argument `n` to perform the following task: (Hint: review what we have learned in Lab 2) 1. Generate a sample from standard normal with a sample size equal to n. 2. Compute the mean of the sample. 3. Compute the standard deviation of the sample. 4. Compute the proportion of values smaller than 1 in the sample. 5. Return a dictionary (Recall Lab 1) containing the three numerical quantities above. c. [2 points] Set the random seed as 1. Run the function stats_normal" with n = 100, 1000, 10000. (Hint: you can simply write three lines of codes. It is totally optional to run a loop.) d. [4 points] Explain in words: what kind of pattern can you see from the results in part c? (Hint: for a standard normal distribution, recall the population mean, standard deviation and proportion of values smaller than 1.) Simulation study plays an important role in statistics and data science. It provides a fundamental tool to study the properties of statistical estimators and models under various situations, because in simulation study, we know the "ground truth" of the data, which we seldom have in real-world data analysis. In this question, we are going to perform a basic simulation study related to the standard normal distribution. a. [2 points] Compute the proportion of values smaller than 1 for a standard normal distribution. b. [7 points] Write a function called stats_normal with argument `n` to perform the following task: (Hint: review what we have learned in Lab 2) 1. Generate a sample from standard normal with a sample size equal to n. 2. Compute the mean of the sample. 3. Compute the standard deviation of the sample. 4. Compute the proportion of values smaller than 1 in the sample. 5. Return a dictionary (Recall Lab 1) containing the three numerical quantities above. c. [2 points] Set the random seed as 1. Run the function stats_normal" with n = 100, 1000, 10000. (Hint: you can simply write three lines of codes. It is totally optional to run a loop.) d. [4 points] Explain in words: what kind of pattern can you see from the results in part c? (Hint: for a standard normal distribution, recall the population mean, standard deviation and proportion of values smaller than 1.)

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The standard normal distribution has a mean of 0 and a standard deviation of 1 The proportion of values smaller than 1 can be computed using the cumul... View the full answer