https://www.nicovideo.jp/watch/sm33601678 https://www.youtube.com/watch?v=8yY4DXFcXko

2. “No one should be ashamed to admit they are wrong,
which is but saying, in other words,
that they are wiser today than they were yesterday”
— Alexander Pope —

5. 2μ + 0(1 − μ) = 2μ
0μ + 2(1 − μ) = 2 − 2μ
μ >
1
2
μ <
1
2
μ =
1
2

6. 2μ + 0(1 − μ) = 2μ
0μ + 2(1 − μ) = 2 − 2μ
μ >
1
2
μ <
1
2
μ =
1
2

7. 2μ + 0(1 − μ) = 2μ
0μ + 2(1 − μ) = 2 − 2μ
μ >
1
2
μ <
1
2
μ =
1
2

8. 2μ + 0(1 − μ) = 2μ
0μ + 2(1 − μ) = 2 − 2μ
μ >
1
2
μ <
1
2
μ =
1
2

9. 2μ + 0(1 − μ) = 2μ
0μ + 2(1 − μ) = 2 − 2μ
μ >
1
2
μ <
1
2
μ =
1
2

11. A B

12.
(σk
, μk
)
lim
k→∞
(σk
, μk
) = (σ*, μ*)
(σ*, μ*)
σ*
σk
(k = 1,2,...)
μk
(x) =
P(x|σk
)
P(u(x)|σk)
(k = 1,2,...)

13.
(σk
, μk
)
lim
k→∞
(σk
, μk
) = (σ*, μ*)
(σ*, μ*)
σ*
σk
(k = 1,2,...)
μk
(x) =
P(x|σk
)
P(u(x)|σk)
(k = 1,2,...)
1 − ϵk
A1
ϵk
A1
ϵk
A2
1 − ϵk
A2
μk

14.
(σk
, μk
)
lim
k→∞
(σk
, μk
) = (σ*, μ*)
(σ*, μ*)
σ*
σk
(k = 1,2,...)
μk
(x) =
P(x|σk
)
P(u(x)|σk)
(k = 1,2,...)
1 − ϵk
A1
ϵk
A1
ϵk
A2
1 − ϵk
A2
μk
=
ϵk
A1
ϵk
A2
ϵk
A1
(1 − ϵk
A2
) + ϵk
A1
ϵk
A2
μk

15.
(σk
, μk
)
lim
k→∞
(σk
, μk
) = (σ*, μ*)
(σ*, μ*)
σ*
σk
(k = 1,2,...)
μk
(x) =
P(x|σk
)
P(u(x)|σk)
(k = 1,2,...)
1 − ϵk
A1
→ 1
ϵk
A1
→ 0
ϵk
A2
→ 0
1 − ϵk
A2
→ 1
μk
=
ϵk
A1
ϵk
A2
ϵk
A1
(1 − ϵk
A2
) + ϵk
A1
ϵk
A2
= ϵk
A2
→ 0(k → ∞)
μk
→ 0
lim
k→∞
σk
= σ* σk
(k = 1,2,…)

16.
(σk
, μk
)
lim
k→∞
(σk
, μk
) = (σ*, μ*)
(σ*, μ*)
σ*
σk
(k = 1,2,...)
μk
(x) =
P(x|σk
)
P(u(x)|σk)
(k = 1,2,...)
1 − ϵk
A1
ϵk
A1
ϵk
A2
1 − ϵk
A2
μk
=
(1 − ϵk
A1
)ϵk
A2
(1 − ϵk
A1
)ϵk
A2
+ (1 − ϵk
A1
)(1 − ϵk
A2
)
μk

17.
(σk
, μk
)
lim
k→∞
(σk
, μk
) = (σ*, μ*)
(σ*, μ*)
σ*
σk
(k = 1,2,...)
μk
(x) =
P(x|σk
)
P(u(x)|σk)
(k = 1,2,...)
1 − ϵk
A1
ϵk
A1
ϵk
A2
1 − ϵk
A2
μk
=
(1 − ϵk
A1
)ϵk
A2
(1 − ϵk
A1
)ϵk
A2
+ (1 − ϵk
A1
)(1 − ϵk
A2
)
μk

18.
(σk
, μk
)
lim
k→∞
(σk
, μk
) = (σ*, μ*)
(σ*, μ*)
σ*
σk
(k = 1,2,...)
μk
(x) =
P(x|σk
)
P(u(x)|σk)
(k = 1,2,...)
1 − ϵk
A1
→ 1
ϵk
A1
→ 0
ϵk
A2
→ 0
1 − ϵk
A2
→ 1
μk
=
(1 − ϵk
A1
)ϵk
A2
(1 − ϵk
A1
)ϵk
A2
+ (1 − ϵk
A1
)(1 − ϵk
A2
)
= ϵk
A2
→ 0
μk
→ 0
lim
k→∞
σk
= σ* σk
(k = 1,2,…)
μk
(k = 1,2,…) μ* = 0

23. See you next time