Here is a distribution of observed values: 0.5, 1.5, 3.5. Construct a kernel density estimation of the probability density using rectangle kernel shape and bandwidth=1.5. Treat bandwidth as half of the rectangle width. Hint: the area under the probability density curve is 1.0. (Do not use the R density function because it does not always treat the bandwidth as the rectangle half-width.) [3pt] How many kernels are used? _______________ [3pt] What is the height of each kernel? _______________ [3pt] What is the probability that a newly observed value will be between 1 and 4