The document discusses probability distributions and Bayesian inference. It provides two probability distributions with four possible outcomes each. It then performs calculations to find the probabilities associated with each outcome and compares the results to determine the most likely distribution.

1. $IBU(15͕࡞੒ͨ͠
ήʔϜཧ࿦ͷ໰୊Λղ͘

4. ໰୊ɿਓͷϓϨΠϠʔ͕͍ΔήʔϜΛߟ͑·͢ɻ
֤ϓϨΠϠʔ͸ʮ্ʢ6ʣʯɺʮதʢ.ʣʯ·ͨ͸ʮԼʢ%ʣʯΛબ୒Ͱ͖·͢ɻརಘߦྻ͸ҎԼͷ௨ΓͰ͢ɻ
͜ͷήʔϜʹ͓͚Δࠞ߹ઓུφογϡ‫ߧۉ‬Λ‫͍͚ͩͯͭ͘͞ݟ‬ɻ
$IBU(15͕࡞੒ͨ͠རಘද
ʘ 6 . %
6
.
%

5. ղ౴ɿ७ઓུʹ͓͚Δφογϡ‫ߧۉߧۉ‬͸ଘࡏ͠ͳ͍
$IBU(15͕࡞੒ͨ͠རಘද
ʘ 6 . %
6
.
%

6. ϓϨΠϠʔͷબ୒ࢶ.͸ଞͷબ୒ࢶ6 %ʹࢧ഑͞ΕΔ
Ώ͑ʹ ࠞ߹ઓུΛߟ͑ͨͱͯ͠΋ બ୒ࢶ.ʹਖ਼ͷ֬཰Λ༩͑Δࠞ߹ઓུ͸࠷ద൓ԠઓུʹͳΔ͜ͱ͸ͳ͍
$IBU(15͕࡞੒ͨ͠རಘද
ʘ 6 . %
6
.
%
ࢧ഑͞ΕΔઓུ

7. ϓϨΠϠʔͷબ୒ࢶ.Λআ֎ͯ͠ߟ͑Δͱ
ϓϨΠϠʔͷબ୒ࢶ%͕બ୒ࢶ.ʹࢧ഑͞ΕΔ
Ώ͑ʹ ࠞ߹ઓུΛߟ͑ͨͱͯ͠΋ બ୒ࢶ%ʹਖ਼ͷ֬཰Λ༩͑Δࠞ߹ઓུ͸࠷ద൓ԠઓུʹͳΔ͜ͱ͸ͳ͍
$IBU(15͕࡞੒ͨ͠རಘද
ʘ 6 . %
6
.
%
ࢧ഑͞ΕΔઓུ

8. ࢒ͬͨબ୒ࢶؒͰࢧ഑ؔ܎͸ͳ͍ͷͰ ͜ͷ࣌఺Ͱ֬཰ΛׂΓৼͬͯφογϡ‫ߧۉ‬Λ‫ٻ‬ΊΔ
$IBU(15͕࡞੒ͨ͠རಘද
ʘ 6 . %
6
.
%
ࢧ഑͞ΕΔબ୒ࢶΛআ‫ڈ‬
ʘ 6 %
6
.

9. ϓϨΠϠʔͷ‫ظ‬଴རಘ͸
ϓϨΠϠʔͷ‫ظ‬଴རಘ͸
4 ⋅ pq + 0 ⋅ p(1 − q) + 3 ⋅ (1 − p)q + 3 ⋅ (1 − p)(1 − q) = (4q − 3)p + 3
2 ⋅ pq + 3 ⋅ p(1 − q) + 3 ⋅ (1 − p)q + 2 ⋅ (1 − p)(1 − q) = (1 − 2p)q + p + 2
ࢧ഑͞ΕΔબ୒ࢶΛআ‫ڈ‬
ʘ 6 %
6
.
p
1 − p
q 1 − q
q
p
0
1
1
3
4
1
2

10. ϓϨΠϠʔͷ‫ظ‬଴རಘ͸
ϓϨΠϠʔͷ‫ظ‬଴རಘ͸
࠷ద൓Ԡ‫ۂ‬ઢ͸ӈਤͷΑ͏ʹͳΓ
φογϡ‫ߧۉ‬͸ ࡟আ͞Εͨબ୒ࢶʹ͸֬཰ΛৼΔͱͯ͠
4 ⋅ pq + 0 ⋅ p(1 − q) + 3 ⋅ (1 − p)q + 3 ⋅ (1 − p)(1 − q) = (4q − 3)p + 3
2 ⋅ pq + 3 ⋅ p(1 − q) + 3 ⋅ (1 − p)q + 2 ⋅ (1 − p)(1 − q) = (1 − 2p)q + p + 2
((
1
2
,
1
2
, 0
)
,
(
3
4
, 0,
1
4))
q
p
0
1
1
3
4
1
2
φογϡ‫ߧۉ‬
$IBU(15͕࡞੒ͨ͠རಘද
ʘ 6 . %
6
.
%
1
2
3
4
1
2
0
1
4
0

11. ͜ͷղ౴ʹ͓͚ΔϓϨΠϠʔͷ‫ظ‬଴རಘ͸
ϓϨΠϠʔͷઓུΛ ʹมߋ͢Δͱ
ΑΓ ͸࠷దͰ͸ͳ͍
4 ⋅
1
3
⋅
1
3
+ 0 ⋅
1
3
⋅
2
3
+ 1 ⋅
2
3
⋅
1
3
+ 2 ⋅
2
3
⋅
2
3
=
14
9
(0, 1, 0)
3 ⋅ 1 ⋅
1
3
+ 2 ⋅ 1 ⋅ 0 + 3 ⋅ 1 ⋅
2
3
= 3
14
9
(
1
3
, 0,
2
3)
$IBU(15͕࡞੒ͨ͠རಘද
ʘ 6 . %
6
.
%
1
3
1
3
2
3
0
2
3
0
1
0
0

12. $IBU(15͕࡞੒ͨ͠
ήʔϜཧ࿦ͷ໰୊Λղ͘