Ө A head teacher wishes to estimate a parameter representing the proportion of her year 6 pupils who will attain the expected level in their upcoming science test. Two teachers summarize their beliefs about . Mr. Wilkes decides that a Beta (20, 8) represents his beliefs, while Miss Green decides that a Beta(11, 2) represents her beliefs. (a) Calculate the mode and variance for both Mr. Wilkes' and Miss Green's prior beliefs about 8. (b) Whose prior beliefs are the strongest, Mr. Wilkes' or Miss Green's? Justify your answer. (c) The head teacher herself does not believe that any one value of 0 is any more likely than any other value of 0. Suggest a suitable prior to summarize her beliefs.

MATLAB: An Introduction with Applications
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Author:Amos Gilat
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A head teacher wishes to estimate a parameter representing the proportion of her year 6
pupils who will attain the expected level in their upcoming science test. Two teachers
summarize their beliefs about . Mr. Wilkes decides that a Beta (20, 8) represents his
beliefs, while Miss Green decides that a Beta(11, 2) represents her beliefs.
(a) Calculate the mode and variance for both Mr. Wilkes' and Miss Green's prior beliefs
about 8.
(b) Whose prior beliefs are the strongest, Mr. Wilkes' or Miss Green's? Justify
your answer.
(c) The head teacher herself does not believe that any one value of 0 is any more
likely than any other value of 0. Suggest a suitable prior to summarize her beliefs.
Transcribed Image Text:Ө A head teacher wishes to estimate a parameter representing the proportion of her year 6 pupils who will attain the expected level in their upcoming science test. Two teachers summarize their beliefs about . Mr. Wilkes decides that a Beta (20, 8) represents his beliefs, while Miss Green decides that a Beta(11, 2) represents her beliefs. (a) Calculate the mode and variance for both Mr. Wilkes' and Miss Green's prior beliefs about 8. (b) Whose prior beliefs are the strongest, Mr. Wilkes' or Miss Green's? Justify your answer. (c) The head teacher herself does not believe that any one value of 0 is any more likely than any other value of 0. Suggest a suitable prior to summarize her beliefs.
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