How to calculate C3_W2_Assignment Exercise 10

[max_mei]

• Week # 2
• Link to the classroom item you are referring to: https://www.coursera.org/learn/machine-learning-probability-and-statistics/programming/uXkeb/loaded-dice

May I know the analytical way to calculate mean and variance for this exercise 10? Thank you.

Exercise 10:

Given a 6-sided loaded dice. You throw it twice and record the sum. Which of the following statements is true?

1. the mean and variance is the same regardless of which side is loaded
2. having the sides 3 or 4 loaded will yield a higher covariance than any other sides
3. the mean will decrease as the value of the loaded side increases
4. changing the loaded side from 1 to 6 will yield a higher mean but the same variance

[Deepti_Prasad]

Hi @max_mei

This should help

C3_W2_Assignment Exercise 10

Thank you for your reply! I wrote code to verify the 4th statement, below is my simple code: def load_dice(n_sides, loaded_number): # All probabilities are initially the same probs = np.array([1/(n_sides+1) for _ in range(n_sides)]) # Assign the loaded side a probability that is twice as the other ones probs[loaded_number-1] = 1 - sum(probs[:-1]) # Check that all probabilities sum up to 1 if not np.isclose(sum(probs), 1): print("All probabilities …