Lecture 6 Finger Exercise

The questions below are due on Friday May 08, 2026; 11:59:00 PM.

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Question 1. Consider drawing a single random sample S_1 from population P_1 and a single random sample S_2 from population P_2. Each sample has size n, and each population has size m that is much greater than n. Assume that the values of P_1 are normally distributed, the values of P_2 are exponentially distributed, and both have the same standard deviation.

Which of the following are true? Check all that apply.

The expected ratio of S_1's standard deviation to P_1's standard deviation depends upon n.

The expected ratio of S_1's standard deviation to P_1's standard deviation depends upon m.

The ratio of S_1's standard deviation to P_1's standard deviation is likely to be smaller than the ratio of S_2's standard deviation to P_2's standard deviation.

The standard error of S_1's and S_2's means are the same.

Question 2. Implement a function simulate_dice_probability(num_trials) that meets the specification below. You do not need to import random; the server will import it for you.

def simulate_dice_probability(num_trials):
    """
    Use a simulation to estimate the probability that the sum of 7 dice is divisible by either 5 or 8

    Parameters:
        num_trials (int): The number of trials to run in the simulation

    Return a list containing the [probability, variance] in that order.
    """
    # your code here

Note: If your test case is failing on the first submit, try submitting again. The randomness of the simulation might be what is causing the tests to fail.