Q1) In the following cell, write the Python code to perform following tasks. 1. Let low=0 and high=(the last two digits of PSU id, if it is o use 10), set mode = (high-low)/2.0. 2. Generate 1000 random triangular random variables using the low, high, and model parameters. 3. Create the histogram of the random variables using 10 bins. 4. Generate 1000 random triangular random variable using the low, high, and mode = (high - low)/4.0. 5. Create the histogram of the random variables using 10 bins. In [ ]: Q2) Which group of the random variables does have more symmetric distribution? The random variables with mode=(high-low)/2.0 or mode=(high- low)/4.0? What is the meaning of mode in statistics? Enter your answers to the following Markdown cell. In [ ]: Q3) Now you will write a code to predict P(X > mode), which is the probability that a random variable will be higher than its mode value. To achieve for this, you need to refer to the previous Numpy reading lab. Below are the steps to achieve this goal. 1. Generate 1000 random triangular random variables using the low, high, and model parameters that you set above. 2. Find how many of those random variables are greater than the mode value (you can use logical indexing for this). 3. Divide the number found in Step 2 by 1000. This is the predicted probability. Predict P(X > mode) for the the cases mode = (high - low)/2.0 and mode = (high - low)/4.0 In which case, the probability is higher? Provide the code in the following Code cell. In [ ]