京都大学 情報学研究科 知能情報学専攻 2022年8月実施 専門科目 S-2
Author
Description
設問1
確率変数
設問2
独立な確率変数
設問3
モデル
(1)
(2)
設問4
ある研究分野における全統計的仮説の中で、真の仮説 (帰無仮説が誤り) と偽の仮説 (帰無仮説が正しい) の数の比が
(1) ある仮説について実験を実施し、有意水準
(2) ある仮説について
Kai
設問1
設問2
By the convolution Rule, we have
By the Binomial Theorem, we can insert
So is the PMF for a Poisson Distribution with the parameter
PS: A easier solution is to use Moments Generating Function.
設問3
(1)
By the Least Square Method, we have the sum of square residuals,
Calculate its derivative with the root
(2)
By the equation (
設問4
(1)
Denote the events below:
- The hypothesis is true:
- The hypothesis is false:
- The test results in significance:
Then, what is asked can be represented by the probability as
By the definition of Significance Level and Statistic Power, we have
Therefore, with the Bayes' theorem, we have
Insert the values, the answer is
(2)
By perform the experiments
Insert the values, the answer is