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.