1 The number of pages being read by a certain person can be modeled as a Poisson random variable with parameter 0, which characterizes the number of pages read per day. Suppose that Carl, being an avid reader of books, noted the number of pages he read per day in the year 2019 and he came up with a histogram of data shown in the figure below. Determine the maximum likelihood estimate (MLE) of Carl's 0, the number of pages he reads per day. Histogram of Data n-frequency of occurence 012 7 X:7 Y:5 XB Y: 2 X: 9 Y:9 10 X: 10 Y: 13 X 11 Y: 17 11 12 X 12 Y: 29 X: 13 Y: 30 13 X 14 Y: 36 14 X 15 Y: 48 X: 16 Y: 39 a. (5 POINTS) Maximum a Posteriori b. (5 POINTS) Least Mean Square C. (5 POINTS) Linear Least Mean Square 16 X: 17 Y: 33 17 0 0.8 0.9 p(0) 0.6 0.4 X: 18 Y: 28 18. X: 19 Y: 23 19 X: 20 Y: 12 21 X: 21 Y: 12 22 X: 22 Y:9 X: 23 Y: 7 23 X: 24 Y: 1 24 X: 25 Y: 2 25 X: 26 Y: 2 Problem 2 (15 POINTS): Suppose that Carl wants to estimate the proportion of books that he likes, denoted by 0. He modeled 0 as a probability distribution given in the following table. In the year 2019, he likes 17 books out of a total of 20 books that he read. Using this information, determine using the following estimation methods: 26