1. You are using the Kernel Density Estimation method with a rectangular kernel to estimate the underlying distribution of your data (X = [5, 1, 3, 1, 2, 3, 5, 5, 6, 5]). The width of the rectangular kernel is 1.2. If we examine the resulting distribution, what would be the area under the distribution/curve (or the estimated probability mass) that is within the range [0, 4]?

What would be the value?

2. You received a dataset about the number of items sold for each of your inventories. It's essentially a sorted list of numbers like this: X = [1, 1, 1, 2, 2, 5, 10, 14, 101, 252]. You decided to use empirical CDF to visualize the data distribution. You normalize your CDF so that the CDF accumulates to 1.0 (the largest value becomes 1.0), then what would be the value of this CDF at x = 100?

What would be the value?