Answered: Let data be x1, . . . , xn. each…

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

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Question

Let data be x1, . . . , xn. each data-point xi is normally distributed, with unknown mean θ and standard deviation assumed to be equal to 1.
As a prior distribution for θ, we assign a normal distribution with mean 5 and standard deviation 10.
(a) What is the posterior distribution for θ? (b) What is the posterior mean for θ?
(c) What is the posterior median for θ?
(d) What is a 95% equal tail credible interval for θ?

X
-.136
.246
1.946
-.786
1.783
1.234
-.02
-.391
-.068
-.103
.718
1.185
-.577
-.292
1.414
1.55
.93
1.397
1.469
1.842
-.351
2.271
-.666
1.006
.499
1.396
.933
-.177
1.656
.762
.709
1.161
.702
.845
-.31
3.184
.47
.437
1.003
1.45
1.836
.867
.163
.867
.541
-.564
-.474
1.464
-1.185
-.37

Definition Definition Middle value of a data set. The median divides a data set into two halves, and it also called the 50th percentile. The median is much less affected by outliers and skewed data than the mean. If the number of elements in a dataset is odd, then the middlemost element of the data arranged in ascending or descending order is the median. If the number of elements in the dataset is even, the average of the two central elements of the arranged data is the median of the set. For example, if a dataset has five items—12, 13, 21, 27, 31—the median is the third item in ascending order, or 21. If a dataset has six items—12, 13, 21, 27, 31, 33—the median is the average of the third (21) and fourth (27) items. It is calculated as follows: (21 + 27) / 2 = 24.

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