Task 1

Sample \(100\) numbers between \(1\) and \(10\) from the distribution described below:

• Probability of getting a \(1\) is \(12/100\)
• Probability of getting a \(2\) is \(13/100\)
• Probability of getting a \(3\) is \(20/100\)
• Probability of getting a \(4\) is \(10/100\)
• Probability of getting a \(5\) is \(6/100\)
• Probability of getting a \(6\) is \(4/100\)
• Probability of getting a \(7\) is \(5/100\)
• Probability of getting a \(8\) is \(9/100\)
• Probability of getting a \(9\) is \(20.9/100\)
• Probability of getting a \(10\) is \(0.1/100\)

Now complete the following tasks:

• Plot the normalized histogram
• Use Chi-square test to see if the null hypothesis stands. Assume a significance level of \(0.05\). Figure 1 contains the Chi-square table.

Task 2

Now repeat task 1 with a sample size of \(100,000\).

Submission

Via Canvas.

• Python file that includes your code for sampling \(100\) and \(100,000\) numbers and plotting the normalized histogram.
• A pdf file that shows the work supporting your assertion whether or not the null hypothesis holds for tasks 1 and 2.