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(Select this problem) {

(Yes)

(No) } No.

大きさ

n

{X 1 , X 2 , · · · , X n }

( Let {X 1 , X 2 , · · · , X n } be a random sample of size n from a normal distribution having the following probability density function. )

f ( x _i ) = 1

√ 2 πσ ² e ⁻

この分布は、二つのパラメータ

μ (

)

σ ² (

)

μ ˆ

σ ˆ ²

ヒント

:

μ

σ ²

( The distribution has two parameters; the mean μ and the variance σ ² . Find the maximum likelihood estimator of these parameters; ˆ μ and ˆ σ ² .

Hint: differentiate logarithm of the likelihood function with respect to μ and σ ² .)