Problem 2 Use any computer programming language (Python is recommended) to simulate rolling a fair...

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Problem 2 • Use any computer programming language (Python is recommended) to simulate rolling a fair six-sided die on a computer. You'll perform the same number of trials as if you were rolling the die physically. To do this, you can use a uniform pseudo-random number generator. Hint: Divide the (0, 1) interval into k bins, i.e. (0.11... (1,1). Each bin corresponds to a specific outcome, just like the faces of a die. When you run a random trial, it's like picking a number from 0 to 1, and you check which bin it falls into to determine the result of that trial. Copy your code here. (20 points) print("Hello World!") • Run B = 100 of simulated experiments and compute X,, for each of these simulated experiments. Plot the histogram of X for this 100 data. Find the value of X that you found using your own physical experiment. Do you have enough evidence that your die was a fair die? Why? Indicate i) the average of these 100 X, ii) your value of X in Problem 1, and iii) the value of k (or k-1) on this histogram and conclude. (30 points) print ("Hello World!") 25 20 15 10 5 0 Histogram of x 5 0 10 15 The mean of the simulated X, b = 1,..., 100 is denoted by a triangle, value of the experiment from Problem 1 is denoted by a cross, while k dentoes the number of faces. Problem 2 • Use any computer programming language (Python is recommended) to simulate rolling a fair six-sided die on a computer. You'll perform the same number of trials as if you were rolling the die physically. To do this, you can use a uniform pseudo-random number generator. Hint: Divide the (0, 1) interval into k bins, i.e. (0.11... (1,1). Each bin corresponds to a specific outcome, just like the faces of a die. When you run a random trial, it's like picking a number from 0 to 1, and you check which bin it falls into to determine the result of that trial. Copy your code here. (20 points) print("Hello World!") • Run B = 100 of simulated experiments and compute X,, for each of these simulated experiments. Plot the histogram of X for this 100 data. Find the value of X that you found using your own physical experiment. Do you have enough evidence that your die was a fair die? Why? Indicate i) the average of these 100 X, ii) your value of X in Problem 1, and iii) the value of k (or k-1) on this histogram and conclude. (30 points) print ("Hello World!") 25 20 15 10 5 0 Histogram of x 5 0 10 15 The mean of the simulated X, b = 1,..., 100 is denoted by a triangle, value of the experiment from Problem 1 is denoted by a cross, while k dentoes the number of faces.

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